Here are the current MLB stadiums that have never hosted an All-Star Game:
Citizens Bank Park, Philadelphia
SunTrust Park, Atlanta (opening next year)
Tropicana Field, St. Petersburg
Yankee Stadium, New York (the new one, of course)
There are also five active stadiums that haven't hosted the game in more than 20 years:
Dodger Stadium, Los Angeles (1980)
Oakland Coliseum, Oakland (1987)
Wrigley Field, Chicago (1990)
Rogers Centre, Toronto (1991)
Camden Yards, Baltimore (1993)
So, with apologies to the next-best candidates Texas and Cleveland --- which last hosted in 1995 and '97, respectively -- you probably start with those venues. Although no offense to the Coliseum and the Trop -- both lovely places to see a game -- but with those two stadiums in flux, maybe we should table them for now.
After four consecutive NL hosts, you'd have to think an American League team would be next. Theoretically, it would be Yankee Stadium, but New York just hosted the All-Star Game at Citi Field in 2013. (This is the problem with opening two new stadiums the same season, New York.) That surely pushes the Yanks down the list. There's a new Rangers stadium supposedly coming in 2021, but other than that, there are no new AL stadiums planned. Thus, of all those AL stadiums mentioned above, the one that looks most likely to me is … Toronto. It will have been nearly 30 years since the Blue Jays last hosted, it'd be a way to celebrate Canada (and further gauge Canadian interest in potentially another team) and it would give everybody an excuse to make sure their passports are updated. Your next AL stadium is probably Toronto.
NL? Well, Atlanta might need a couple of years to get its parking situation settled and figured out. Wrigley Field can host anytime, and you have to imagine, once all its construction is done, that it zooms up the list. (Particularly if the Cubs win a World Series sometime in the next few years.) But it looks like, in an immediate sense, it's a battle between Los Angeles and Philadelphia. Since Commissioner Manfred has already met with Dodgers officials -- who would certainly pony up in a bidding process -- I'll make them the top NL bet. But with more NL stadiums prepared to host than AL stadiums, the wait might not be that long.
So, my official predictions for the next, oh, 10 All-Star Games is as follows (the first two are the confirmed ones):
2017: Marlins Park, Miami (confirmed)
2018: Nationals Park, Washington (confirmed)
2019: Rogers Centre, Toronto
2020: Dodger Stadium, Los Angeles
2021: Citizens Bank Park, Philadelphia
2022: SunTrust Park, Atlanta
2023: Unnamed Rangers Stadium, Arlington
2024: Wrigley Field, Chicago
2025: Yankee Stadium, New York
2026: Camden Yards, Baltimore