https://kriii.com/
There's an area with a glass floor where you can stand over the exact spot where they found his body.
There are also some Roman ruins in Leicester although I'm not sure if they've finished restoring them.
Bosworth Field, where Richard III was killed, is not far away and pretty interesting.
https://www.bosworthbattlefield.org.uk/
You might want to take a look at Coventry Cathedral, which is famous for being hit by bombs during WWII -- the old bombed out structure is still there, alongside a newer modern cathedral.
https://www.coventrycathedral.org.uk/visit/visit-coventry-cathedral
If you're going to go to Coventry, there's also Warwick, which doesn't have a cathedral per se, but does have a large collegiate church.
https://en.wikipedia.org/wiki/Collegiate_Church_of_St_Mary,_Warwick
And if you're going to go to Warwick, Kenilworth Castle is definitely worth a look:
https://en.wikipedia.org/wiki/Kenilworth_Castle
Finally, it's kinda far out of your way to the north west, but if you're interested in Roman ruins then Chester is a great place to visit. It still has much of the old Roman defensive wall around the main city center, in good condition -- you can walk on large parts of it. Plus it has a cathedral
https://chestercathedral.com/