The offshore fishing grounds are usually quite a long ways... Bay fishing in the area is great... Especially if you are going to be by yourself, chartering a boat for yourself could be costly whereas a charter for a bay boat should be under $200...

You wouldn't go to Cabo and shorefish, sometimes you have to work with what you have. Redfish, snook, and sea trout are plentiful and tons of fun on light tackle.

I did a quick Google on "deep sea fishing port aransas" and got several hits Here's one from Dolphin Docks http://www.dolphindocks.com/summer.html "60 Hour Fishing Trip $390.00 Boat departs 6:00am Tuesday. Meals are provided. This is a deep-water trip going out for Wahoo, Dorado, Yellowfin and Blackfin Tuna."

I've never been on any, hopefully someone with direct experience will weigh in with a recommendation

My friend, Nate is now operating Iced Down Sportfishing. My brothers went by last weekend to see the new boat and said it was awesome! I'll tell them to write up a report after their trip. They have all fished with Nate before and a great time. His website is www.iceddownsportfishing.com