City costs can be cut down with courthouses, Versailles, or the Forbidden Palace. When you start setting up far flung cities you gotta get one of the above three in them or else they get stupidly expensive. Also, make sure your existing cities are doing as well as they can. Make sure you have workers improve every possible tile around a city so that it stays profitable - put down tons of cottages. You never (well, 99.9% of the time) want a city working an unimproved tile.
You can also rebuild the palace in a more central location to cut down on maintenance, since maintenance increases with distance from the capital.
Really though, the cottage thing is what killed me for a while when I first started playing because I had mixes of farms and cottages around my cities. Wrong. With few exceptions (GP farm, specialist economy, etc), ~every~ grassland tile within your cities fat crosses should be cottaged up (grassland because the 2 food allows your city to sustain growth while working the cottage).
For example, when I start a new city I assign a worker to that city. The first thing they do is get any food resources up or build a farm to allow the city to grow faster. Then I get it connected to the empire with a road, then improve other resources, and then cottage the hell out of every remaining square.
Another important point is to not over rely on water tiles. If you're a financial civ and you've got a lighthouse then every coastal or lake tile gives 2F and 3C, which is a great deal early game when compared to a paltry 2F 1C from a grassland cottage. However, by working the cottages you make them grow and make them ridiculously profitable (particularly after Printing Press), gaining you 2F and 7 or 8C from a town, and even a hammer if you run the right civic. So even if water tiles will carry you through the early game, by the mid game you'll be seriously lagging in both tech and wealth unless you've moved onto something more lucrative.
