Born and raised Houstonian here. Texas is definitely tough to beat in terms of quality of life and how far the dollar goes (although it's slowly leveling out with other states to an extent). I'm slightly biased because I'm from here (and Houston specifically) but there's obviously good and bad to it. In terms of income, tax, quality of life, and certain liberties you will love Texas compared to Illinois. It won't even be close.
Weather in Texas is dependent on the area you're living in. Houston has mild winters and hot summers (with an assload of humidity pretty much year-round). Austin gets hot too and stays slightly cooler in the winter than Houston. Dallas is drier year-round and actually hotter than Houston during the summer, and gets colder in the winter. North Texas has the most "seasons" out of anywhere in the state.
As for Houston, this place is completely whatever you make of it. It's not the prettiest and people certainly don't move here for the climate, but the culture and people here make this place awesome (to me). The quality of life and things to do here are great as well. It's a unique place in that it is absolutely massive and very spread out. Instead of having one main "downtown" like most cities, we have like 8 (Downtown, Galleria/Uptown, Midtown, Greenspoint, Energy Corridor, Med Center, etc). The food here is second to none due to it now being one of the most diverse cities in the States. We have a good bar/club scene if that's your thing. There are a ton of parks/green spaces around the city, dog parks, running/biking trails along the bayou, etc. Lots of great museums and outdoor things to do (when the weather isn't 95+). Our economy stays fairly strong as well thanks to it being fairly diverse in terms of industries. We're definitely not a tech hub though (unless you count the medical center which is the largest in the world).
If you have any specific questions though, I'll be happy to answer whatever I can
