Won't you be my neighbour? ;)
Seriously, I live in Hyattsville, MD, just outside DC, and it checks all your boxes.
-You can definitely rent a 2br apartment for under $1800, or less if you don't mind basement apartments.
-I can walk to parks, the public pool, Aldi, post office, CVS, Latin american restaurants, fast food, dry cleaner, bank. If I lived a mile farther east, I could walk to Yes organic grocery, brew pub, yuppier restaurants, gift shops, and African restaurants. Library, shopping center with Target etc., and bigger grocery stores are all about a mile away, Home Depot another mile beyond.
-I'm a 10-minute walk from the metro, and many bus lines stop within a block or two of my house.
-Hyattsville itself, while walkable, is not super bike-friendly, because there aren't a lot of bike paths and there is a lot of on-street parking. OTOH, on the non-major streets the traffic is low so biking is still pretty safe and unstressful. And there is very easy access to a large network of bike trails--you can go to Bethesda or down to Nationals Park or to the waterfront in DC or into DC. Although as a woman I would not ride the trails alone after dark.
-There are farmer's markets in all the neighboring towns, including some pretty big ones. Some are close enough to walk or bike to. We also have CSAs, Hungry Harvest, and organic food co-ops nearby.
-Fun activities: free DC museums, all the DC tourist attractions, local festivals, waterfront activities, film fests, local arts district, two universities within 3 miles, ....
-Winter is chilly rather than cold, often around freezing but rarely below for sustained periods, little snow. Having lived in Michigan you will be astonished at how paralysed the region gets when there is a significant snowfall. 18 inches (winter of 2016) closed the schools for a week, but that hardly ever happens.
-Diversity: the east side of town is more yuppie, and mostly a mix of whites and blacks; farther west is a little more blue-collar and is a mix of Hispanics and whites; still farther west there are a fair number of African immigrants. Not very many Asians. People seem to get along well; I haven't heard of any racially-motivated incidents and I see people of all hues enjoying themselves together in public places.