The Cubs last hosted an All-Star Game at Wrigley Field in 1990. The only current MLB park that previously hosted a Midsummer Classic that’s had a longer hosting drought is the Oakland Coliseum, which last hosted one in 1987 — and I’m pretty sure you can understand why there isn’t going to be another one at that stadium.
There are two current stadiums that have never hosted an All-Star Game. One is Tropicana Field in St. Petersburg, Florida, and again, the Rays are likely not going to host the Midsummer Classic until they get their stadium situation sorted out.