When my family and I go to the cities we usually stay at one of the Mall of America hotels–plenty of restaurants, shopping, and Camp Snoopy are right there. Plus, it is very easy to get on the light-rail train at the mall and it will take you right to the Dome. You don’t have to switch trains, and can avoid traffic and parking issues.
A lot depends on how much you want to drive. Yes, there are advantages to staying out by the Mall, but then you have to drive into town and pay for parking. Or, you can stay in downtown, and get free shuttle service to and from the Dome, or walk.
I should also say that the train is only a few bucks per person and also somewhat impossible to get lost with. The MOA is the last stop to the south and all the stops are clearly marked. Even a Yankee fan could figure it out.
I would stay at the Holiday Inn Metrodome (612-333-4646). I worked there for 3 years. Its a nice place and offers courtesy shuttle to and from the Metrodome. Its a 14 floor hotel that offers a nice view of downtown (ask for to be upgraded to a “view” room especially if you are a priority club member. Click Here for their website. Talk to Ruby in reservations. Book it now to get a better rate. Ask for the best deal!