I have an unorthodox idea for where it should be located. The idea is that it should be everywhere. It should be a travelling Hall of Fame. Similarly to a travelling circus. Imagine a Hall of Fame exhibit that's always on the move. The schedule for it should be a separate state and city each or every other month. The eligible cities would be every city which has an SHL team.

A travelling Hall of Fame is better in every way to a stationary one.
1) It enables every fan that lives close to an SHL city to visit the Hall of Fame. Instead of forcing everyone to travel to one specific location. Which can cost fans thousands of dollars.
2) Because of #1 more people will visit and bring in more ticket money and more merchandise sold.
3) When the Hall of Fame moves to a new city/state it would be made an event which will bring more attention to the league.
4) It would create more jobs. One set of jobs for those that follow the Hall of Fame around wherever it goes. And another set of jobs local to the city it's in at the time for setup and teardown.
5) It would improve the local economy of each eligible city because of the attention and influx of tourists.
6) Having the Hall of Fame stay on each location for only a month would still make it an exciting event even though it's a recurring one. This means the Hall of Fame would visit each city once every 18 months. Making it a novelty and something to look forward to each time.

On top of all of this. The teams in the league are very well located to allow for a travelling path that won't really create any detours or wasted gas(except Tampa). See below for my suggested path.