Progressive Field — originally Jacobs Field, opened 1994 — is the home stadium of the Cleveland Guardians baseball team, and one of the early wave of "retro classic" ballparks that helped revive American downtown baseball in the 1990s. The asymmetric outfield, exposed steel beams, and view of the downtown skyline beyond left field have made it a model for stadium design ever since.
The Guardians play April through September; cheap upper-deck seats are easy to come by, and the food in the concourse (especially the Slyman's corned beef stand) is well above average. Stadium tours run on non-game days and are worth taking if you have the time — they include the dugouts, the press box, and the field itself.
Tickets through the Guardians' website; the stadium is walking distance from any downtown hotel.