Hi everyone!
Sorry for not replying sooner. Great advice all around. I recently switched over to Bureaucracy, which heavily boosted my hammers (I also removed some scientists and worked some of the grounds with hammers and lumbermilled a forest tile). So now my capital has a good amount of hammers 10+ as well as still being a research city (oddly enough, my industrial-focused city, which is coastal, has now also become tied as a good research city).
As I said before, I don't even consider myself to have even a "moderate" skill level. I'm still learning new stuff every game, and frankly, I don't know how you guys can play and remember all this stuff without your heads exploding!

When the map starts getting crowded and I start having like 20 resources and 5 or 6 cities, I start to loose my grip on what I'm doing. I'm sure that will come in time. Right now I still feel very overwelmed.
Let me try and address some specific things that people have pointed out. Please let me know if my strategies are unsound.
That's an awesome science city, except for those plains. Did you move the settler? It would have been better to place it 1 tile east, so you could work the gold, oasis & extra flood plain, with a plains hill & forest for production. Nothing you can do about it now, though.
If you build a forge & assign an engineer specialist, you'll have 4 base hammers + 25% from the forge (5 total.) Running Bureaucracy will add another 50% hammers & commerce. Universal Suffrage will help, but you're a long way from that. You can also farm or cottage the plains tiles, or work the forests instead of running specialists.
That's about it as far as your options go -- it's the nature of science/commerce cities to be low on hammers. Like it or not, you'll have to

to really get infrastructure in there...that's what slavery is for, use it!!
I did not move my original settler, and I couldn't see the gold before I chose to settle (my first turn). All in all, it's not a disaster because I culturally flipped one of Alexander's cities that currently is close to that gold and can directly use it.
I'm having great success at culturally flipping cities this game. I've taken 3 of Alexander's (kept two, disbanded one) and one of Mehmed's)
Slavery is your friend.
Cottage plains tiles and work those. One hammer each, no worse than building an expensive temple you didn't need just to run a Priest. Which brings up what you're actually doing with your two measly hammers per turn...
Why is there a monument in your capital? I really hope you've still got an active Stonehenge in another city, because there's no reason your capital needs one. Same for the theatre, you don't need the happiness, I doubt you need that culture, and you aren't running artists. That courthouse that cost you quite a few hammers (and many turns) is saving you a whopping one gold per turn...your capital doesn't need one, at least not that early. You've got a barracks there, but I can't see why you'd want one in such a hammer poor city unless you're whipping troops. And the temple of course...again, don't need the happiness, and there's better ways of getting one hammer than running a Priest...unless you built Angkor Wat somewhere, or just really want a Prophet.
It looks to me like your biggest problem isn't the lack of hammers (although that is an issue), it's what you're using them on. Where's your aqueduct while you're wasting 3 food per turn being unhealthy? Think about what your city really needs before deciding on what to build. In a city making so few hammers, it needs to be building the things it really needs (AQUEDUCT), not missionaries for other cities.
I moved away from slavery so that I could take feudalism for the specialists. Besides this city, I don't really have a need to whip out buildings/units, but I might reconsider. Specialists have paid off because I've already had 3 great artists, a great scientist, and a great prophet (gotta love Philosophical leaders).
I do have Stonehenge in another city. I built it because I wanted to have it (Celts weren't in the game, so England should have it!) I know that's a silly reason, but it did help out with some early culture expansion in my cities.
Courthouse is an error on my part. I can see that now. I will be more mindful of that in future games. I built the barracks because Alexander started as a
very close neighbor, and I was weary of any sudden attacks he might launch. Temple was to get enough temples to build the religious building that adds +50% culture to a city. I now (having played some more after my original post) have an aquaduct in the city. Good catch on that one!
it's been said already but I feel the need to repeat it loudly :
YOU DON'T NEED MORE HAMMERS.
I'd switch away the priest for one more scientist, and that's it.
You're researching MC in 1000AD+, and that not good.
You need to research more before anything else.
You have enough forests to chop for the university you're going to want.
If you don't use slavery in this city, you won't get enough hammers to make up for the lost commerce.
edit : one more thing
You don't need barracks, walls and what nots in a city producing 2 hammers
Walls were there to get the castle for the +1 trade route. The reason I'm reasearching metal casting is for guilds (knights) to defend my northern cities against Mehmed and Stalin. No one would trade it to me (or no one had it). I was far above metal casting at the point of the screenshot. I was just filling in a pre-requisite at that time. Right now (currently in the game) I have Redcoats at about 1300 AD, so that's not too bad from a technology standpoint. Right?
Thank you all for your advice. Keep it coming! I need all the different viewpoints I can get. I'm thinking of going for a space victory this game, or possibly a cultural, though I don't know if it's too late to try for that.
How long do you guys keep slavery? I usually drop it around this point in the game to start focusing less on infrastructure and more on city size / economy. Is that a bad idea?
Thanks again!
