Tim and I have visited the recently refurbished City of St. Paul, MN Rice and Arlington Batting Cages, see also www.rabattingcages.com. The address is 1500 Rice Street, Saint Paul 55117, Phone (651) 558-2255.
Hours are on the web site, 12-8 Mon-Thur and 12-8 Fri (varies). Sat is 10-6 and Sun 11:30-5:30. There's abundant parking.
There are four cages, adjustable from 40 to 70 mph. One is softball-only, the others can be softball or baseball. One cage can be reserved for $22/30 min or $43 for an hour; you need to reserve over 24 hrs in advance. Cage reservation is suited to groups.
Other cages are open to all. The lines can be very long at peak times, but things are quiet from 12-4. In my limited experience you don't want to arrive after 6:30 pm.
Tokens cost $7 for 5, $1 apiece with a St Paul School photo ID (Jan-Jun). You can get a bit of a discount with a 22 round card.