There is some good information and some misinformation here already. Hills, if used well, can actually improve your economy. Engines are most efficient when loaded, it's when you're cruising at low load that you have a poor thermal efficiency, because at low load your cylinder pressure is lower at part throttle and you're creating a lot of vacuum, both of which are wasteful. It's only when you add stop signs to hills that you have a recipe for poor economy.
My first recommendation is to get some instrumentation to monitor your gas mileage. An MPGuino will be most accurate for determining miles per gallon but is a little more difficult to install than just plugging it in, and it lacks the ability to read things like the temperature sensor, AFR and percent load as the computer has calculated it. Your other options are an Ultragauge or a Scangauge, which will plug directly into your OBD port.
Add a bit more air to your tires. Don't go over max sidewall (for safety reasons!) but if your tires say "42", put 40 in them, not 30 like it says on the door jam. Higher tire pressure generally improves wet weather handling (raises speed at which you hydroplane, for one) at the expense of a slight grip loss in dry weather, which I'll take any day of the week. Underinflated tires are a hazard in poor conditions and may rob you of a few MPG.
Saving fuel in a city environment is largely an art of slowing down efficiently. Sometimes it's good to DFCO (if your car supports it) and sometimes it's not. When you're accelerating up a hill it's generally good to keep the load higher and the RPMs lower (say, 2000-2500), but not load it so high that the car's computer begins to enrich the mixture. You're not going to know when this is by feel, but a safe rule of thumb is "50-75% of the pedal position at which you don't get any more power". If you're in a gear that is decelerating you even at WoT, you're in too high a gear. When you get to the top, if you see you're going to need to stop at the bottom, DFCO down the hill and take advantage of getting to the bottom with zero fuel used. If you won't need to stop, coast in neutral and take advantage of that potential energy you put into your car getting it to the top of the hill. Using the engine to brake down a hill is like riding your brakes, you're turning all of that good energy you burned in getting up the hill into heat and brake dust (or friction and vacuum inside the engine). If you need to get to the top of the hill going a little slower, so you're not speeding too much from coasting down, do so.
Try to pick routes that won't have you stopping a lot, even if they're just a little longer. You may find you'll burn less fuel taking those.
When on the highway, your only real tool for improving economy is by slowing down. I've found that in my car (before I did any modifications) I can get 37MPG at 65mph, 33MPG at 70, 30MPG at 75, and 28MPG at 80.
Other than that, know that when your car hasn't warmed up, it's going to deliver worse economy. Don't be surprised if you find trips of under 2-5 miles with a cold engine will net you less than 20MPG, regardless of what you as a driver do. I find it's better to take a bike if the weather is nice for short trips.
You can find some other fuel saving tips over at Ecomodder.com, they have a "
Ecodrivers Ed" section for talking about things like this. The Aveo isn't actually all that great a car for saving fuel, but I can think of two members right now that are averaging about 35 and 40 (mixed driving) without using any weird techniques or doing anything dangerous like drafting.
Using these tips, the best I've seen is 51MPG city in a car rated for 23:
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