Lived in the area off and on for like 30 years, own property there. If it were me I would stay in PI, you can get a lot better bang for you buck in terms of accommodations. There are some nice water front properties for rent in PI nowadays. And you don't have to hassle with all the parking BS on the Island if you take multiple vehicles.
Only on the weekends will there be some traffic on the causeway, and even then it will only be late in the day headed west, off the Island.
For an extended stay in the area I much prefer Port Isabel due to the Island crowds. If you plan to spend a ton of time on the beach, which few people seem to do, then I would say stay on the Island. Quick access to the beach is the only advantage I can see for staying on SPI vs. PI. Prices in PI are about 30% to 40% less than PI (I have rental property in the area FWIW) and the hassles are less. Just my opinion.