Beginner Urban Sustainable Homesteader here. There is LOTS you can do but some of the best ones do take a little investment. The upside of that investment is that most of them are significantly positive gainers if you should ever sell the house.
Given your location, you may be in a good spot to get a solar hot water heater rather than electricity panels. A nice Evac tube system, rated for 65 gallons (20 tube SunMaxx) blended into your existing hot water heater can provide significant savings
over the long run and give you independence from other supplies. This system is meant to be "handy owner" friendly in terms of installation. And instead of 10K plus needed to do much with electricity and stay within aesthetics needed to sell again, you can get this very attractive and useful system for 2 to 3 grand, 1600 if you do the installs yourself.
The green roof idea is great, but if the roof wasn't originally designed for it, you can have serious liability issues so check thoroughly with your insurance first!
Naturalize and cultivate all that yard. Anything not under the plow can be naturalized so that it takes less water and maintenance. Blend permaculture into that and it is a double whammy of good for nature and good for you.
Remember the drip! If you don't have it already, install rain diverters into 55 gallon barrels at your downspouts for the gutter system. You'll get a bounty of good stuff for your garden. If you are forced to run AC then install barrels or 13 gallon trash cans below the drips for them. Because of high humidity here (and the intense smoke from wildfires forcing windows closed) I am collecting 20-26 gallons from my split system every single day.
Check into the rules for bees in your area. Many places simply forgot to put that into their agricultural restrictions. Here they didn't so it is a no-go, but even a single hive is going to be great for your garden and a bonus of honey for you.
Dual use trees and decorations. Instead of standard plantings when I built, but in order to stay in good with my neighborhood, I made sure almost all of my plantings are dual use. A sprawling rose has great hips. Bayberry gives visual interest and gives me bayberry and scented foliage (and some pest control). Mulberries (which were accidental) are now being tended for shade during summer and fruit during spring. You get the idea.
Since you are looking now with that in mind..remember to study the position of the home with regard to exposure, shade during different seasons and so on. Southern exposure is great, unless it is only on the front of the house without proper eves during summer. Be sure it is hitting the right spots.
Keep us updated on your search and good luck