Dinner before Hamilton tonight

I'm not sure if this is what you are looking for, but the first time I ever ate at a Shake Shack was after Hamilton at the Victoria Palace theater in London.
It was very convenient amd open late. That was 2018, so I'm not sure if it's still there. I can tell you, though, that we were far from the only post-Hamilton patrons there! They had quite the little late rush.

(Oh, and btw, I don't know if this is in your plans, but the actual Hamilton souvenirs seemed extraordinarily expensive to.me. £50 for a Hamilton logo'd no-brand name waterbottle, iirc.)

Nearby and casual: Wok and Fire, Franco Manca, Pizza Pilgrims.

Wok and Fire is Asian fusion fast casual with a small seating area. Franco Manca and Pizza Pilgrims both have more patron seating. Franco Manca’s deal is their sourdough crust. Pizza Pilgrims is rated up there with Pizza Express, and I love their pizza. Wok and Fire is fun and fast and fresh. I haven’t tried their new corndog menu, but I am looking forward to it!

All are very close to the theatre.

Are you looking for fast food or a restaurant with table service?

The Ivy Victoria is a 5 min walk to the theater and takes reservations. You can order from the regular menu or the 2 course menu for £20.95.

There is a shopping gallery near the theatre called Cardinal Place. Full of choices for all kinds of food: https://www.atvictorialondon.com/en/food-drink?page=1&sort=asc&filters=d6d5a702-975d-4436-8615-ac7dd9e694b9&replace=1

We ate at Nando's because I love piri piri. Casual, fun, good value.