There are many "cool" areas. I think we all think that our area is cool.
I would agree to see where work is located. Houston is sprawling so yes you can be in traffic for an hour or more EACH WAY. I live inside of the beltway, which is by no means the 'burbs and work downtown. My commute is not bad but yesterday it did take me an hour to get home and that was at 4:30 in the afternoon.
For some people this is ok, for others it is not. If it regularly took me an insane amount of time to get home or to work I would lose my mind. If that is ok with you, then it isnt a big deal. We do have people that work here that live in The Woodlands and that are in traffic 2 hours a day each way.
Traffic is bad here, yes some routes are better than others but if you live outside of the city and have to get into the city on a regular basis you will get into traffic and sit in it for a good long time.
As a secular homeschooler I have found that the outskirts of the city have more religious homeschoolers than secular ones... and most of the events, museums, etc. are located inside of the city.
However, houses are cheaper outside of the city. For what I spent on our house one of my friends got a house three times the size. They are mostly cookie cutter homes in planned developments but if you want cheap houses outside the city is the best place to look. I would advise to do your research on the newer homes because there have been problems with shoddy manufacturing and many builders have gone out of business or gotten sued recently. I have an old ranch house built in the 1960's that comes with its OWN problems but it is what works for us and I believe in having a smaller carbon footprint.
Sorry for the novel here, but really it is all about what your family likes and what your priorities are.
I lived in the Montrose area where we could walk to things, the houses were old, it was very liberal, GLBT friendly, and secular. We loved it but we could not afford it anymore when the prices got incredibly high to live there. So for us the priorities were still close to the inner part of the city but for a price we could afford.
If you give us more specifics about your situation we might be able to help more in getting you where to look.