Beachside Villas has 1, 2,3 bedroom units on a beach and their contact is :

Yolanda 313 884 7706 at 40 Webber Place Grosse Point Shores, Michigan

There's a website: beachsidevillas.com for more info about amenities and floor plans.

The location is a nice long beach but near the airport runway. The positive is you could enjoy watching huge planes land or watch huge yachts leave the lagoon.

I don't think you could walk to any nightlife but it's nearby. Walking the beach infront of the villas you have Karakter's a beach bar serving food, Mary's Boone with a dining room.

Don't know much about Mary's Boone accommodations you might try their website.

But bottom line is I doubt you can find much for $2000. more like minimum 350 + per night.