Hello NB -
Welcome to Texas.
In between 20 year stints of living here in Corpus Christi I lived in Houston for about 20 years when I was transfered there by my company. I hated the thought of moving to the big city with lots of traffic but once there I loved it. Same goes for some others who are friends of mine.
First ..... Humble and League City may not be on completely opposite ends of the spectrum but they are close to that. Humble is a nice area that is north/northeast of Houston. Lots of tall pines and golf courses. League City is southeast of Houston and is much closer to the gulf than Humble. Other than that I don't know much about League City.
As far as gulf fishing goes out of Galveston and Freeport is concerned the fish we catch may be similar and the methods used to catch them are the same but the big factor is the weather and the water. Along the Texas coast the beaches and the water are not the same as you'll find in Florida, particularly Pensacola/Destin. We have a lot more wind than most areas of Florida and that means rougher, dirtier water. We have to pick our days.
Not until some time in July will you be able to plan trips in advance with a greater certainty of going. This weather usually lasts into September but tropical activity in between will create interruptions.
You didn't say if you owned your own boat or if you fish charters and party boats. If it's tuna you like there are several options. One of the best options is the Big "E" out of Freeport which offers multi-day trips that target Yellowfin Tuna. There's usually a mix of AJs, groupers, snapper (in season) and Blackfin Tuna also on these trips. They are having a 76 hour trip during the fourth of July that many of us are going on. It should be a blast. There are other party boats out of Galveston. If you trailer your own boat you may want to consider pulling it to or storing it somewhere near Freeport.
Spinning tackle is common inshore here. Inshore we catch a lot of Kings, Dorado, Bonito, Spanish Mackerel, Ling (aka Cobia in Florida
) and some folks target Tarpon. There is the rare Tripletail too. Further out we catch the tuna, Wahoo and AJs. Even further guys go for billfish.
For what it's worth a very close friend of mine moved to Pensacola several years ago and he still swears the fishing is better here than there but that may just be him .... I dunno.
Hope your move goes well. You'll meet lots of fishing friends right here.