The weather is great in a sense that it's warm, but be prepared for sweltering heat and humidity for ~340 days of the year. Especially during the summer, it's hard to be outside for more than a few minutes without needing a shower.
Lots of outdoors stuff to do like you mentioned, especially water-oriented activities. If you surf, New Smyrna is the most consistent spot but even that's not nearly as consistently good as it is consistently sharky.
High speed internet would be no problem. Brevard and the surrounding areas are red but I wouldn't necessarily consider it cultural backwater. You'll be exposed to a much higher number of crusty beach people (especially in Cocoa Beach) than you will rednecks or similar.
We get a disappointing degree of "people who disagree with me are stupid" here at times.
Many would be surprised by how inexpensive it is, but in my opinion (like much of the US) the area suffers from poor planning. Recently two buildings one block from the beach were torn down to make room for a parking lot. Plus there is a NIMBY / anti-development contingent which basically kills off any renewal efforts. Prime real estate has gone undeveloped because of height restrictions.
With that said, I do think it could be a good area for startups. There is a lot engineering talent, the quality of life is good compared with the cost of living. Plus there is access to a major airport in Orlando with direct flights to SF, LA, NY, etc.
Personally I'd really like to see more startup activity in the Cape Canaveral/Cocoa Beach area.
I have a coworker with a house at the edge of a swamp. He likes to go out in his airboat and shoot alligators. He likes to set off explosions. I have another coworker, from San Francisco actually, who has sheep and can shoot his AR-15 in his yard. Trump has dropped by twice, at the MLB airport. The lines of adoring fans went for miles, and there were only about 5 protesters total. My workplace has a giant (maybe 15x7 foot) US flag in the cafeteria, and every year we hold a military-style flag folding ceremony. Everywhere you go, there are engineers who work for defense contractors. There is a stand-your-ground law, and our wonderful Sheriff Wayne Ivey has some great videos on youtube about the need for armed citizens prepared to shoot all kinds of bad people.
For those of you who aren't horrified, we're hiring for low-level hacker stuff... but the rest of you need to stay right where you are. You'd be unhappy, and you'd make us unhappy.
The idea is to assemble a small group of talented folks. Even digital nomads who want to do a short stint would be welcome. And then solicit contracts, or start New Space ventures.
Main benefit is of course proximity to rocket launches ;) For which we could host viewing parties, outdoor BBQs, photo shoots, etc.
Region is known for relatively cheap rents (compared to South Florida). Great weather. Year round golf, tennis, scuba. Not sure about high speed internet availability. And it may be a cultural backwater. But that only leaves more time for building ;)