I went to Houston on a business trip in late June once - and I don't recommend June! Walking from hotel to rental car at 6:30 am, and my glasses fogged up by the time I got the car, and my blouse was sticking to me. Hair went all funny-looking too (I have straight hair, but ended up with curly fly-aways). It was so hot and humid that walking to a restaurant just down the street wasn't a good idea - better to take the air-conditioned rental car. I've never had my glasses steam up so much like that. It was kind of funny actually. My husband and I had a few laughs over this. "Can you see yet?" and stuff like that.
A couple of years later, my husband and I went for a fun weekend getaway to Austin in March - and it was *lovely*. Not too hot, and not too cold. It wasn't 'summer-y', but more like trench coat or light jacket weather. We had so much fun. Walked all over the place and the weather was just about perfect for sight-seeing and enjoying ourselves. I'm not a fan of overly hot weather, so that might colour my perceptions a bit. For me, anything over about 70F is 'too hot'.
So I guess it also depends on what kind of weather you like and are used to, as this will help determine which times of the year are going to be comfortable for being out and about, enjoying the sights and so on.
