Munich

Regensburg & Amberg perhaps.

Check out Bamberg
https://en.bamberg.info/

Regensburg is one of my favorite towns for just the things you mentioned.

If you want something a little closer, there is Landshut. Perhaps not great for shopping (no expert here) but the Augustiner restaurant near St. Martin's Church and the Landshut version of the Hofbräuhaus are both decent restaurants. The town is colorfully scenic and Landshut even has a castle. Its tourism is not that well known to Americans.

I agree with Regensburg. If you want a smaller place, what about Augsburg and Rosenheim?

Mittenwald.

I second the Bamberg suggestion. Beautiful town with lots to see and do for a day.

I wanted to know if there was a neat town that had shopping, food and very quaint to visit nearby.

Bamberg, while very nice, fails in the "nearby" end of things. It almost 2 hours away by ICE, and that makes it a very expensive day trip. By regional train, that you should use to make it a reasonably priced day trip, it is 3 1/2 hours away.

Something quaint, old fashion, maybe out of the way with a Bavarian feel.

Bamberg, while in the state of Bavaria, is really in Franconia, and does not have the stereotypical Bavarian feel most tourists imagine. Mittenwald would fit the bill, as would Oberammergau, as well as a number of other locales.

as Lee said, Mittenwald. Quaint, old centre with frescoes painted on buildings, easy to walk around, fantastic scenery around it. And a brewery with pub and restaurant (and tours if you can get there for 1030 on a Tuesday).

http://www.brauerei-mittenwald.de/english/index.php

get a Werdenfels Ticket, day pass for up to 5 people. first costs €20, the rest €6 each on a group ticket (do not buy 1 ticket each!!). Also valid on Munich S Bahn trains for connections at Hauptbahnhof and Pasing. Oddly, not subject to 9AM restriction ilke most regional offers. Sadly they lost the english webpage https://www.bahn.de/p/view/angebot/regio/regionale-tickets/bayern/regio-ticket-werdenfels.shtml

area map https://www.bahn.de/p/view/mdb/pv/deutschland_erleben/allgemein/tickets/2017/mdb_251855_werdenfels_ticket_karte.pdf

I find it weird that Regensburg, while marvelous, is being called quaint. It was once one of the largest and most powerful cities in the Empire. It's old and well preserved, but far from quaint. Ditto for Augsburg.

Personally I like Schongau but I am partial because I read the "Hangman's Daughter" book series, which is set in Schongau.

Don't use hotel Monaco by train station terrible!