It helps a lot to have some screenshots for a discussion, so I took the liberty of taking some. I also removed a lot of the out-of-date signs and added new ones and made a few minor changes, so please use the attached saved game.
Starting us off, it looks like the island to the SE sucks... it has no Food Resources. However, upon closer inspection, we see that the possibility of a Cultural Bridge exists if we settle a City there.
Besides, settling even a junky City here = +1 Commerce in each of our other 10 Cities, meaning +10 Commerce per turn, minus the Maintenance Costs. At Prince difficulty level, this extra City will be totally worth it even as a junky City.
What do I mean by a Cultural Bridge? Well, look at the signs... the "No Food or Commerce" sign is what you typically see for an Ocean square that cannot exist within a fat cross. However, the "Ocean with Food + Com" (where Com=Commerce but the sign didn't fit my text) location has 1 Food and 1 Commerce showing. That means that that particular Ocean square is in the potential fat cross of some potentialy settleable piece of land... which means that somewhere to the north, east, south, or west of that square must exist a Coast square.
We can see that there isn't Coast to the north or to the west, so therefore, there must be a Coast square to eitiher the south or east of there. If we settle on top of the Marble, we will create a Cultural Bridge to said Coast square. Since we are Creative, it'll only take a couple of turns to create such a Cultural Bridge, which may open up additional AIs for us to meet or at least the possibility of finding another landmass to settle.
What that means is that we will want to
bring a Settler and a Worker to that island. I would simply Cottage the 3 Grassland squares within the City's fat cross using the Worker.
After dropping off those units, we will want to get a Military Police unit (say, a Warrior or a Chariot or whatever). Once we have the Military Police unit, we can take the Scout and the Galley and head to the SE to see what else we can find down there.
As you can see from all of the Unhappy faces, Unhappiness is our NUMBER ONE issue right now. We have ZERO Happienss Resources and there is no Religion within our empire, nor known by any of the AIs that we have met (which only just happens to be one AI).
So, we need a way to get Happiness ASAP. St. Petersburg has finished building a Forge and we also recently finished hooking-up Stone. The Pyramids give us access to the Representation Civic, which can be run to solve a lot of our Happiness issues.
In an effort to speed-up The Pyramids, I recommend that we send one of our Workers to Chop the 3 nearby Forests. The sooner that we can complete The Pyramids, the sooner that we can switch into Representation and the sooner that we'll be able to grow our Cities larger without worrying quite as much about Unhappiness issues.
In the meantime, growing faster doesn't help us much. I would strongly consider
whipping the Library in Moscow. Once we have built a Library there, we should
hire 2 Scientists, since growing into Unhappiness really isn't going to give us a lot of value at this point.
Yoshiville can continue to pump out Work Boats for the 2 Cities to the NW as well as some Chariots to act as cheap Military Police units. Archers are slightly cheaper but we don't have Archery and it's not worth teching Archery right now. Also, Warriors are even cheaper, but we have Copper connected, so Chariots for Military Police units will be what we will use.
The Great Person Farm should work on preparing itself... Granary, Lighthouse, Forge, and Library would all be good to build there so that we will be ready to build The National Epic when we finally tech Literature (that tech will be a long time in coming).
Other Cities like Yakutsk and the Cities in the SW can build whatever you want... most of them have started on Granaries but if you'd rather go to war with Alex (we REALLY DO NOT need Barracks to go to war), then you could instead queue up some Axemen instead of Granaries in our auxilliary Cities. The goal would be to have a stack of 10 units (Axemen and/or Chariots) before we attack, so that when we do attack, the war will go smoothly. This decision is your choice: either build Granaries and other infrastructure like Lighthouses and Libraries or else forget about the Granaries for now and build Axemen in Cities like Yakutsk and our 3 south-west Cities, as well as our eastern City once it is done building a Settler.
As I said, Barracks will be overkill right now, so if you choose the war path, you won't be building Barracks and the war won't actually start until someone else's turnset.
Here are those three Cities in teh south-west... like I said, we can either build infrastructure or switch to building Axemen. Rostov should at least finish off the Work Boat. If we go for infrastructure, then Rostov can hire 2 Scientists after building a Library... but it could equally just pump out Axemen.
Actually, Cities like Yekaterinburg and Whale Flipping would probably be better off building Chariots instead of Axemen, since both Cities are low on production. Feel free to whip out some Chariots out of these Cities if you do decide to go for the military units path.
If you want to be really sneaky,
you can stop the "xplorer" Work Boat from moving and use it to net Yekaterinburg's Fish, then use the newly-built Work Boat that gets built in Rostov to explore to the north. It's a minor point really and will only gain you a bit more Food and probably a bit faster exploration, so if you forget to do so, no worries. Every little bit helps, though, so if you remember, great!
We recently learned Writing and it appears that we have a coastal trade network connection with Alex. These facts mean that we should
Open Borders with Alex. We also have 3 extra Pig Resources... I would
trade a Pig to Alex. He doesn't have anything to offer in return, but he'll like us more. It's not like we can do ANYTHING ELSE with those extra Pig Resources, since we haven't met any other AIs.
Actually, along those lines, Alex's Espionage spending on us makes it look like he hasn't met any other players, either.
This belief means that we should probably not tech Alphabet next. If an AI is isolated from other AIs, it won't trade techs with you unless it is Friendly toward you. Trading Open Borders and trading him a Pig Resource (without getting anything in return) will definitely help in getting us toward Friendly, but it'll be a long way off--it probably can't happen with just these trades alone and we'd probably have to share a Religion or a Favourite Civic with him. Neither of us have a Religion, so that idea is out. Since we're going to try to build The Pyramids, we'd rather run Representation instead of Alex's Favourite Civic of Hereditary Rule, so that idea is out, too. Plus, he would have to learn Monarchy before he could run that Civic, and he's probably a long way off from that tech, seeing as how we are playing on Prince difficulty level.
Sooooooo... I would rather chase after a Happiness-enabling tech. I see two main options: Monarchy and Calendar.
Of those options, I prefer Calendar. We have Incense (a Calendar Resource) and if we settle a City in the SE later, we can also get a Dye Resource (a Calendar Resource).
Monarchy is one of the few techs in the game (in BtS anyway--it didn't used to be this way in Civ 4 without expansions aka Vanilla nor in the Warlords Expansion) that an AI will trade to you even if it doesn't know any other AIs. So, it's much better to get this tech in trade, since, eventually, even if we are isolated with just us and Alex, we'll be able to get it in trade--while in the same isolated circumstances, Alex will NOT trade Calendar to us.
Also, we don't even have Mysticism, so Monarchy is several techs away... and we'd probably prefer to get those Religious techs in trade at some point.
Finally, Monarchy opens up improving our Wines for +1 Happiness and Hereditary Rule... but since we're building The Pyramids, the Hereditary Rule Civic will not only be redundant with building The Pyramids (since The Pyramids enable the Hereditary Rule Civic as well as other Government-line Civics), but we won't even be running Hereditary Rule as a Civic, since we'll want to run Representation instead. Thus, I would
tech Calendar next (meaning that Math will get automatically chosen as our next tech).