Gloomhaven has great monsters to play with. Ii thiink Arkham Horror (?) does too. Bloodborne boardgame has some beautiful pieces.

Any of the tactical-ish table top ones will have minis. However the quality and type vary wildly. As has been said warhammer 40k, fantasy and age of sigmas have great stuff buts really expensive. There are games that come with their own standies and minis but those tend to be a bit underwhelming (unless you like to paint them).

For my money I’ve had really good luck with after market Etsy type products that I’ve purchased for a game I found and enjoyed.

I’ll also give a big second to pathfinder (1 or 2) and starfinder. The art is amazing.

Wh40k is know for its copious minis

Pathfinder has boxes of cardboard pawns. There is really great art on them.

In terms of wargames (tabletop games where you control armies of miniatures against your opponent to score objectives and points), Warhammer is the most mainstream, 40K for the sci-fantasy version and Age of Sigmar for the more Tolkienian fantasy one. But I recently got into Star Wars Legion and boy is it a fun game. If you like the setting, Legion is highly recommended.

In terms of pure boardgames, my favourite ones miniature-wise are Bloodborne and Mansions of Madness.