The Cubs have hosted three All-Star Games in the event's history: 1947, 1962 (the second of the two games that year) and 1990. The Cubs probably would have had a game in between 1962 and 1990, except that starting in 1971, TV networks wanted the game at night, and of course Wrigley didn't have lights until 1988. Once lights were scheduled to be installed, MLB quickly awarded an All-Star Game to the Cubs.
In this earlier era the only event other than the game itself was the Home Run Derby, then in its infancy. Much like this year, early July weather in Chicago in 1990 was cool and wet. A cold front had gone through Chicago the night before the Home Run Derby at Wrigley -- the event was scheduled for daytime. With the wind blowing in at 20-plus miles per hour, only five home runs total were hit in the event, and Ryne Sandberg won it with three. He was the last hometown player to win the HRD before Todd Frazier did it this week.
Rain blew into the Chicago area during the game, which was an offensive dud. (You'll note that boxscore calls field conditions "soaked.")
This photo shows where they were in the game when a torrential downpour halted play for a little over an hour:
The A.L.'s first two hitters in the top of the seventh singled and then the rain hit. As you can see, the N.L. had only one hit at the time of the delay and wound up with just two. The two hits is still the record for fewest hits by one league in an All-Star Game, and the 2-0 game, which ended just after midnight, was pretty dull.
Nevertheless, the Cubs will surely want another All-Star Game at Wrigley once all the renovations are complete. The game is now three days' worth of events showcasing baseball. MLB also hosts a FanFest somewhere in the host city with exhibits and lots of stuff you can spend money on (of course).
Now that the All-Star Game is no longer awarded on an alternate-year, alternate-league basis but instead is opened up for bids, you can bet the Cubs will likely bid on one, but wouldn't do it before they make sure all the renovations are complete and everything's working properly at Wrigley Field. The Cubs hope to have everything done at Wrigley by Opening Day 2019, but I'd guess they probably wouldn't put in any bids before the 2020 or 2021 game.
The next three All-Star sites have already been awarded: San Diego in 2016, Miami in 2017 and Washington in 2018. MLB would probably like to have a game in Tampa, as the Rays have never hosted one, but aren't likely to do so until the Rays solve their stadium situation. Beyond 2018, the only parks that have been built since 1990 that won't have hosted an All-Star Game are Citizens Bank Park in Philadelphia and the new Yankee Stadium in New York.
If the Cubs bid on and receive the 2020 game, that'd make exactly 30 years since the previous one, just about appropriate since there are now 30 teams. The current parks with the longest waits to host other than Wrigley are the Rogers Centre in Toronto (last hosted in 1991) and Camden Yards in Baltimore (last hosted in 1993).
Here are a couple more photos I took during pregame at the 1990 All-Star Game, of the players in each league lining up for their team photo: