I like Windsor Park. The homes there were built in the late 50's through the 1960's, so if you don't want a fixer upper, you're going to have to find one that's already had the work done. There are lots of large trees and many have hardwood and/or tile floors. BTW, even though you don't want a fixer upper, you might want to consider a home that would be a good candidate for solar panel electricity. Austin Energy has one of the best rebate programs in the country, and lord knows, we get plenty of sunshine!
I like using Austin Home Lisitngs because you can search by neighborhood:
There are still many neighborhoods in Austin that you can buy a home in priced under 200k. I would like to know more about what you are looking for in terms of size, number of beds and commute so I can point you in the right direction. If you want to be close in to downtown I suggest area 10N which is still affordable and an easy commute to downtown. Feel free to contact me so can better understand your wants and so that I can send you some properties you might be interested in.
Great place! If you have a $225K budget, you could get more...
This all depends on your lifestyle. If you want to be close to downtown and don't mind a more sketchy area, try 78702 in East Austin. If you want a little safer, 78723 (Windsor Park, University Hills) is safer and has more family appeal. East Austin schools are still a slight issue, but the area is still growing.
Another area not mentioned is Crestview/Allandale. Great area, very hot and growing. Zip 78756. I've reviewed many of these areas and written about them. Depending on your lifestyle, you may choose to be closer to downtown or central Austin. You don't have to be in the suburbs to buy under $200k.