I mean if it tells you anything about how good it is, I would still have a hard time deciding between Hamilton and something else even though I've seen it twice and have tickets for 3 more dates. I just don't know how I'll ever pass up an opportunity because I love the show so much.
But if you can't get tickets to Hamilton if I were you I'd wait a bit to get tickets. I know some people hate the color purple but I personally loved it--I went in Chicago with low expectations and ended up going back and taking others. I'm extremely excited about the cast and I definitely am going to make it a point to see this. I am really really hoping allegiance will be good but there is a small part of me that's really worried it's going to be terrible.
Based on the shows you've listed I assume you're going in November or later so school of rock and fiddler may also be possibilities.
Aside from hamilton I doubt any of these are going to be impossible tickets so if I were you if I couldn't get tickets to Hamilton I'd try to wait until the previews start to see what the buzz is. (Obviously that depends on your timing.)
Also I'm not sure if there's a reason you're choosing only one, but if it has to do with scheduling it's worth noting that there are a lot of time periods when Hamilton has a non-traditional schedule. I am going on a Sunday night in the fall and a Monday night in the spring, which is really exciting because most other shows are dark and I am not foregoing the opportunity to see something new to see something I've already seen 3 or 4 times. It's worth looking into if you want to try to sneak in another show. Of course it could just be you don't want to spend all your time and money in theater so then this advice isn't real helpful. :)