A couple of suggestions that you might not be doing.
1. At any level above monarch, you won't be able to out research the other AI, so you have to be an active trader.
2. You'll probably trail in tech in the middle ages, unless you have the Great Library (then stockpile cash for military or trades). So try to stay close to the tech leader via trading. Try to pick the techs the AI normally rates low (Printing Press, Medicine...) and use those techs to swing 2 & 3 fers (example trading Printing Press + $ for Banking, then PP + Banking for Physics, then Physics back to your original trading partner for $), you can pick up 2-3 techs and end up with more money in the bank.
3. I'm not sure which government you prefer, but for non-war games, you'll need to be in either Democracy or Republic to keep up a solid cash flow.
4. Add money & tech producing improvements (banks & universities) to your larger cities.
5. Improve all tiles being worked. Each road in more $$ and rails add more food/shields to each city.
6. Try to build a pair of productive cores. One around your capital and another around your forbidden palace. If playing Vanilla or PTW try RCP.
7. If you find yourself behind a couple of techs in the Industrial Age and can't get TOE, go for Espionage and try to steal your way to parity. This can start wars, so be careful when and where you steal.
8. Watch the size of your army. If you own your entire landmass and don't have any ROP's going then you don't need garrisons on interior cities. Each unit costs gold. Once rails are in place you really only need coastal defenders and 4-5 good attackers to eliminate invaders. The AI is very poor at across ocean invasions.
9. If you find yourself at war with an AI with better units, build artillery. A stack of 20-30 cannons, supported by rifles for defense and cavalry for attacking can take a size 12 city with 3 infantry with few losses.
10. When all else fails, try to steal a UN victory by saving a GL or setting up a pre-build and tech stealing your way to fission and build the UN. Setup MPP's with everyone and get #1 AI to goto war with you and let them attack you first. The other AI will dogpile on #1 and you'll get their votes when the UN is built.
Just a little 10-pack of things I've learned watching the Guru's & Master's play the last couple of years.
One other thing, check out the SG thread for a training game by Ghengis Khan & Sir Bugsy. It's got 50+ pages of discussions on how to improve your gameplay.