There are several different approaches to what you want to do, and it really depends upon your calendar:
1) Hop out of Galveston and sail directly, non-stop. This requires a constant watch, and possibly/probably
radar. You can sail in the
safety fairway to avoid the rigs, but you will have to dodge traffic - that likely won't see you or move for you.
2) The
ICW. This will take a while - probably 5 days minimum. It does let you stop for the night. It's not a bad trip, just a little boring after a while. You have 2 sets of locks, both of which should be open with no recent rain - but still require coordination with the lock keeper. This is also your best alternative if you have more than 20kts of
wind offshore. The gulf is ugly above 20kts. And, for the past 2 weeks, it's been above 30kts. If you do this
route, make SURE you invest in unlimited towing with Towboats US or SeaTow.
3)
Offshore hops. You can make day hops, offshore, spending the night inside. The following are good recommendations: Galveston:
Freeport: Matagorda: Port Aransas: Port Mansfield: Port Isabel.
Of course, you can also do a combination of 2 & 3 - and that would probably be my recommendation. Again, I would avoid the gulf in more than 20kts, especially since the gulf is new for you. I'd WAY rather spend time in the Atlantic at 30kts, than the Gulf at 25kts. Wave periods of 8 seconds compared to 22 seconds is huge. Try passageweather.com for decent predictions. If in the Gulf, ALWAYS have a plan to come back inside, and remember that inlets can be difficult when it blows.
And one final thing: Get your hands on a Campbell's Guide - even an old one. There are several on fleabay.