You're off to a good start having looked around the area physically. The location of the Heights area is attractive because of its access to Downtown, Galleria, etc. I recommend viewing a couple of homes in that area to see if what you look at, is something that you will be comfortable living with. While some of the homes may look similar from the outside, it might be a different story regarding the interior. Also, regarding values a lot depends on which one you are interested in, that can be compared with those that are similar (sq. ft, year built, number of rooms, etc).
It seems like you are still not quite set on the area of town. Are you particular about the commute, schools, type of living, access to certain amenities? Once you prioritize what is really important, you might be able to make some adjustments. If you are flexible and would like to look for a larger home in the suburban area, I could make some suggestions, but I would have to know what your priorities are, although ultimately it will depend on you to make your final decision.
Good Luck with your home search and have a great start to this New Year. Best wishes.