I just finished the main quest for the Minutemen. I'm still on good terms with the Railroad and the BoS but I'm not getting quests from Maxson or Desdemona.

I have settlements everywhere I can have a settlement.

I'm pretty much the benevolent overlord of the Commonwealth at this point.

Is there anything else worth doing before I start up a new character?

Try to find all locations in the game and see if there are any random quests to encounter. Build up a settlement as much as possible. Those are just some ideas.

1. Go to Diamond City to enjoy the view of your flags and troops (sometimes may take up to a week to appear). Also read Piper's article

2. While you are there, you will get a post-MQ quest "In Sheep's Clothing"

3. Finish any remaining quests or personal story elements (after the MQ, I had my character find new love and visit any locations he did not visit before)

4. Since you are the Minutemen General, why not turn some settlements into "proper settlements" if you haven't already. By that I mean having a city hall, barracks, guards in proper uniforms, etc. Also you might have fun giving special roles to settlements (my Institute character formed cities, research stations, Minutemen Outposts, etc.)

Time for "this is my boom stick" and kill everything you see. Hail to the king baby!

The short answer is not really. The true answer is: it depends on what you want to do. There is no proper post-game questline or anything of that nature, so you aren't going to miss out on something you could only see at the conclusion. I personally enjoy "living" my character. Once the game is complete, I get most of my fun out of roleplay and that typically involves building up my settlements, scouting out new places, keeping the raider/super mutant/ghoul population in check, stockpiling weapons and ammo to outfit guards at my settlements, and the list goes on. I am about 10% done playing a Bethesda game when I get through the main quest, and that usually takes me a good 40-50 hours, if not more.