Thompkins Barracks is sort of within walking distance of downtown Schwetzingen. The walk is easy, but can take quite a bit of time. For those who would rather not walk, you can take bus 710 from one of the bridges adjacent to Thompkins Barracks. The ride will cost roughly 50 cents.
In May and June, you will get Spargel (Asparagus). Schwetzingen is famous for its awesome Spargel. Try it in restaurant Kaffeehaus, or Cafe Journal at the Schlossplatz.
Cantina Mexicana, Schlossplatz 8a. A centrally located Mexican restaurant only several meters from the castle. The food is decent and the service is effective. A cheap happy hour is a major selling point for this bar with cocktails going for as little as 4 Euro a pop. But don't expect much of a Margarita. The decor elicits of the stereotypical Mexican restaurant with bricked walls and bright neons that advertise beer.edit
Da Dona, Marstallstraße 18, ☎ +49 (0/6202) 1 26 81 52 (+49 (0/173) 30 91 36 6, fax: +49 (0/6202) 2 35 73). Daily from 5:30PM - Midnight (Kitchen open until 11PM). A small, but good Italian restaurant, family owned, quaint/elegant atmosphere, food is great, service is very kind and professional.€20. edit