Keep in mind that I am not a very good player so my advice may not be optimal.
I just loaded your save and from what I can see, you did some good things and some not so good things.
First off, the Social Policies: you invested 2 SPs in Patronage but you do not have any City State as ally (or even friend), if you want to go Patronage you should do the Quests (from what I see you did one for Vatican in the past but that has faded and your influence has dropped to the point you are not even friend). You should have finished Liberty instead, that Great Person of your choice is very good. Since you are at Prince level and you can basically get most wonders, you can so choose a Great Scientist and plant an academy (early game that can mean even 20% science boost -or since you are Babylon and already have an academy keep it for mid/late game to bulb), otherwise you could choose a great engineer and rush a game changing wonder like Petra. Of course in other situations you could chose a different great person (for example a great prophet in order to fund/enhance a religion, or a great admiral to explore the world and be the first to meet every civ).
City Placement is good, growth is important and your cities can grow fast. I would have put Akad one tile NE next to the mountain: you do not lose any resources and you can build an observatory since it will be next to a mountain. Also I would have considered building Dur-Kurigalzu on the wheat, on coast; this way I would have access to sea and can improve 2 fish tiles and with a Lighthouse that would mean 5 food + 1 production (with fishing boats) plus and an extra 1 production + 1 gold (with harbor and seaport) per fish tile. You will lose the hill sheep and you settle on wheat but having a city on the coast may just be worth it.
Another city spot worth considering for Dur-Kurigalzu is between the lake and coast (3 tiles NE of the actual position). You lose the ability to build the water mill and hydro plant, and also lose access to one sheep, but you gain an extra fish early game (totaling 3) and cow (which may be better than sheep). You could also get the dyes if you settle before Morocco (and buy the necessary tiles) - or steal land with a great general.
Overall the city placement is not bad. You should not worry about the number of cities. Each city you build increases your social policy cost AND your science cost for each tech, so any new city should be worth the increase cost for both. You can win a science victory with one city at any difficulty (you can also win with 2 cities, 3 cities and definitely 4 or more cities), so don't worry about that: four great cities is a lot better than 4 good cities and a crappy one.
Having said that you might notice that Tradition is very good for a 4 city (or less) empire. Tradition is actually a very strong Social Policy Tree and you can use it for empires with a small number of tall cities but that does not mean you cannot expand beyond 4 cities. Overall tradition is a very good SP tree, especially when you are stating civ 5 (liberty, honor, and piety starts require more delicacy in order to make them work, and honestly I have not been able to do a good start other than Tradition or Liberty).
Regarding Wonders and National Wonders: You have some nice wonders, you got the Oracle which will help you fill out a social policy tree (which you did not - but I already mentioned it). Pyramids is decent if you went liberty (especially if you do not "steal" workers form other civs or City States).
On Prince you could have gotten more Wonders but I would not advisee to get in the habit of building too many wonders since on higher difficulties you will not be able to get many.
Regarding National Wonders you should prioritize National College in Brave new World. It is very important, coupled with growing your capital, as it will give you a lot more science and you will be able to keep up with the AI on higher difficulties (on Prince you may not notice it, but from Emperor up you will notice the AI is ahead of you and often reach renaissance or even industrial eras before you do - you usually beat them to modern era). Building it on turn 170 is way too late. Try building it earlier, prioritize libraries in your first cities and build the NC as soon as available.
The National Epic build is very good: it should be built in a city that has the guilds, lots of food (to work the guilds), and a garden to stack with National Epic; this way you get the maximum great artists/writers/musicians generation, and since you can only get these Great People by working the associated Guilds (and have only 2 specialists for each type of great person in the whole empire), this is important.
Regarding specialists, you should be working the scientists specialists. Just by working the 4 scientists in Babylon and Akkad you will shave off a turn in researching steel. In the long term that cam mean a lot more (plus you get to generate a great scientist) As soon as you research Education, prioritize building universities in the bigger cities first, and working the specialist slots. Also the guilds specialist slots should be worked as soon as possible (they generate culture, and great persons that can also generate culture + tourism), with the possible exception of the Musicians Guild (for culture victory games). You can work the engineer slots if you want to generate a great engineer (always use the great engineer to rush wonders, planting a manufacture is not worth it on most situations), otherwise working a mine is better (of course if none is available you can work the engineer slot for extra production but be careful not to generate an unwanted great engineer since that will delay great scientists). Working a merchant slot is very tricky since generally you do not want a great merchant (it will only delay great engineers and scientists). In my opinion the gold bonus from either settling the great merchant or using it for trade missions is not worth delaying the great engineers or scientists (maybe for Venice it is worth it but note every time).
Tech wise are good, Philosophy (for National College) and Education (for Universities and scientists) should be prioritized early game, and after that Scientific Theory (for Public Schools) and Plastics (for research labs). When you enter renaissance you should invest at least 2 Social Policies in Rationalism (the opener and secularism), that will keep the science rate up.
Regarding defense you are exposed to a potential attack from Morocco. Having your main "army" around the capital does not make much sense since Arabia would require lots of turns to cross an army over that rough terrain (just leave the horseman to protect both Babylon and Nippur against barbarians). Build more archer units and toughen up the East side of your empire. A scout in the north jungle will do well to see an approaching Arabian army and react accordingly.
Diplomatically, you have made some pretty bad deals with Arabia, and you are now in negative gold (I assume you bribed them not to war on you). If you declare war you will lose the research agreement, but get your gold per turn in the positive and also some resources to sell to others. You will also lose 2 caravans which is bad, so you might as well just wait it out. If you declare war, build some defensive army at least.
Early on, internal trade routes are much better than external ones: sending food to capital and growing it outweighs the Gold per Turn and Science per Turn you might get by using that caravan to trade with the AI. Use your 2 remaining trade routes to send food to capital (ideally you should use all four)