We have discussed the RV thing also.....
We have a storage unit in Illinois that the boy uses (and we pay for), and we have one in florida here... that we need to sell everything out of it....
But we have been thinking, when the sister-in-law finally gets her HUD housing, we are going to sell this house and buy an RV, set it up on a lot, and start selling everything we have out of the storage unit.

The sister-in-law is Bi-Polar and we are attempting to get her set up for a decent life... then we are off to discover America....

Not going to buy one of those half-million dollar RV's, just a good used one with maybe one pull out....
No kids, no pets, just two small units to rent so we don't have to buy clothes everytime we move.

Only downfall I can see is having to empty the darn septic system.... and replacing tires.... guess we will have to save up some cash somehow for the little glitches in our plan

Ditto to what Springman said about costs. I've been to the big island a number of times. If you take the time to work all the arrangements out yourself you will make good wages in doing so because you will save lots of cash. Be creative about everything.
Last time the wife & I went to Puerto Rico for 9 days (2 yrs. ago) we spent $2800.00 total for lodging, flight, food, car rental & all. We had a ball. But I acted as our travel agent. It would have easily cost twice that through a commercial agent.
Hawaii is a little more expensive though. Flights & lodging especially. You might be able to get it below your 5k figure a little; but not a lot. Hawaii is more expensive period; than PR & PR was much more receptive to tourists than the Big Island. At least that's what I found.

I think I'd be bored living on any island ,same roads to ride time after time . The lower 48 states and Alaska still offer miles of beauty and places I haven't seen.