You won't find too many places for parking your TT that will be "near" Wrigley Field.
However, one option might be to stay in a nearby hotel and park your TT in the hotel parking lot. I realize that this defeats the entire reason for wanting to take your TT to Wrigley Field, but maybe this allows you to have a "nearby" tail-gate before or after the game.
Another option might be to camp at Illinois Beach State Park (located near Zion, IL on Lake Michigan; north of Wrigley Field). See
DNR. Reservations can be made on-line at
Campgrounds and Camping Reservations - ReserveAmerica
If you stay at Illinois Beach State Park, one way to get to Wrigley Field would be to take the MetraRail (Metra Union Pacific North) and transfer to the Chicago Transit PURPLE train, which will take you to Wrigley. See links below for routes/schedules.
1. Depart at Zion, IL MetraRail Station.
Metra Union Pacific North (UP-N) Station
2. Exit MetraRail at Evanston DAVIS Street.
3. Transfer to Chicago Transit PURPLE train at DAVIS
CTA Purple Line - Route Guide (Map, Alerts and Timetables)
NOTE: the PURPLE train will take you to Wrigley only on WEEKDAYS. For weekend games, you'll need to transfer from the PURPLE train to the RED train at Howard Ave Station.
PURPLE TRAIN INFO:
CTA Customer Alert Details
RED TRAIN INFO:
CTA Red Line - Route Guide (Map, Alerts and Schedules/Timetables)
4. Exit either the Addison or Sheridan stations.
For more Information call the RTA Travel Information Center: 1-312-836-7000.
Open 5 a.m. until 1 a.m. every day.
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