Rushigan, don't know if this will help much, but I'll give my two cents since not long ago i was in same predicament.
My wife and I recently stopped in at Westwood to check it out. Its off of 59 and honestly its not
surrounded by the best area, but once you get past that the course itself as well as the practice area looked pretty nice. On the Saturday that we went they were having a junior tournament which I thought was pretty cool - if maybe you have siblings or nieces/nephews that may be a feature you want.
However there was also a turn off for me there. While I like that the place seems to be all about the golf, and the staff seemed engaging and attentive, I didn't get the best vibe from the members that were around. There were more than a few of them that were either walking towards me, or I made eye contact with, and I would say hello and they either wouldn't say anything or mumble something quickly and move around. Maybe I ran into all the guys that lost in their foursome that day, or I just caught them in a bad mood, but that was completely the opposite from what I have experienced at my home club when I was
checking it out. Hopefully most of them aren't like that, but unfortunately the ones I encountered were.
I haven't had the chance to check out Braeburn, but would like to. Ive heard good things about it.
I've been a member at Golfcrest in Pearland for nearly 2years now, and I love it. Its been a great place for a beginner like me to learn, but there are also a bunch of good players there as well. The greens are usually in great condition compared to many of the surrounding courses, and at the moment they have a project to extend a number of the tee boxes for those that play from the tips. The junior dealI got involved no initiation fee, so that was a big plus. It is a country club versus the golf purest places like Champions, Westwood, etc, but its not one of those places where a bunch of social activities overshadows a terrible course. Plus I have yet to encounter a single ****** bag out there. I don't know if I've been extremely fortunate, but all the members I have met - long time or newer ones like myself, have all been engaging, helpful, and personable. I will be honest and say though that the pro shop and the dining room are dated if you care about that sort of thing. They recently renovated a lounge area on the second floor for watching games and stuff, but the rest of the building is still behind on that. But to echo West, I'm guessing its about 30 minutes from where you are in downtown, so I don't know if that's worth the drive for you or not.
As far as the earlier comment about Champions, I played there months back and it was in decent shape - as I recall a bunch of courses in the Houston area had issues with the greens because of the late winter or something, so I did see a few spots here and there. But nothing serious. That place is amazing to me. From the locker room that feels like a museum to having a passing conversation with Jackie Burke. It just feels like you're not only out for a round of golf, but walking in a historical landmark. If you really feel like that is the place, you can bring your handicap down (I used a thread on this board called the Ultimate Practice Routine, and this year went from a 20+ to a 14.6). It's been a few months since I've been out there, but I was under the impression that since they got the former superintendent of Redstone, the maintenance has improved greatly.
Another one that is a similar distance from downtown as Champions (roughly 30 minutes) is Kingwood Country Club. They have 4 courses on site and every time I've played out there they are in good condition. I think you can even pay a little bit more of a premium and join Deerwood right up the street. Considering they are owned by Clubcorp, that will give you the occasional variety if you want to switch it up a bit. Since they just bought Canongate that should about double the amount of courses they have in the Houston area.
Also, on the way to Champions on 1960 off 45 is Northgate. I've never played that course, but I think that they have a partnership with Walden on Lake Conroe, so you should get privileges there as well.
I just know that there are 3 nines, so that helps from a variety standpoint.
I know I just wrote a novel, but basically much of it depends on how far you want to drive from downtown. If you have enough free time where a 30 minute trip doesn't bother you, that helps your options.