Hungryjacks is nice for Gunflint trail riding, otherwise there are a number of places to stay in Grand Marais that are nice for Northern North Shore riding all the way Down to Lutsen.
If doing the mid-section of the NST and Tomohawk, Crooked Lake near the Trestle INN is awesome.
If Doing the Vermillion area, I would stay on the west side and head North from Cook in terms of riding. There are lots of places to stay since the trails are all connected but the Casino on Vermillion makes for a good time. If East end of Vermillion, Ely Grand Lodge, or rent a cabin. Giants Ridge also has very good accommodations and sits on the Taconite trail.
Crane Lake, North of Vermillion has a great place to stay, the Voyagaire. If staying even further North near Ash-Ka-Nam, you have the Ash trail lodge and serveral other choices on the river there.
Last but not least, consider Grand Portage Lodge and Casino if thinking about hitting the best trails in the state IMO.
Other things to consider where to stay. There are really only a few cities of any size on the IRON Range/North Shore. Grand Marais and Lutsen have the most to offer on the North Shore while Virgina/Eveleth is your largest city on the Range. Places like Ash Trial and Hungry Jacks are remote and offer a very serene setting so if quiet and relaxing is what you want, they are a great choice. More nightlife, bars, restaurants are available in Grand Marais and around Virginia.
I've ridden up there for 25 years and don't proclaim to be an expert, but in my experience, you can get the best of both worlds anywhere North of Duluth and have a great time either soaking away the miles in peace, or taking on the town.
PS: As a former Duluthian, I would offer this often overlooked option. Duluth has direct access to the North Shore Trail, the Island Lake area trails, and trails to Virginia. It makes for a great place to ride out of as well and still has some bigger city ammenities.