We recently got back from a two night trip to Prague, Czech Republic, a 5.5 hour drive from Trier. There is a TON to do and see in Prague, no matter the season. We went during "high season" which I would not recommend, seeing as there are lots of tourists. We did our fair share of shoulder rubbing.
Hotel: I recommend staying in "old town," for there is lots to do, all within walking distance! Hotel Cloister Inn is inexpensive, cheap parking, breakfast provided (nothing fancy), and has spacious rooms. The location is perfect, right in the middle of Old Town (close to Bethlehem Chapel) with restaurants and shopping right around the corner. The hotel itself is nothing fancy, but again, good location (fabulous little restaurant right around the corner - Restaurant U Plebana).
Must-Sees: Charles Bridge (both during the day and night), the Prague Castle and (only some) of it's entities, a live jazz show (we went to one at Grand Hotel Praha and USP Jazz Lounge - food was AMAZINGGGGGG at Grand Hotel Praha, atmosphere was better at USP), Jewish Ghetto (including the cemetery), view the river and castle at night, walk in every church you see throughout the city.
Restaurants/Foods: The Czech are known for their Goulash soup.. I, being vegetarian, did NOT have any. Czech meals seems pretty hearty - meat and potato kind of people... again, not me, but the area offers a wide variety of foods. Also, taste the Original Budweiser and other Czech beer and wine while you're there (A enjoyed Kozel Dunkel).
* Prague is a big city, expect to walk, or use the city's public transportation which is reliable and inexpensive.
* Cheap, cheap, cheap! Food, drinks, etc, all inexpensive.
* When driving, be sure to stop at the border and pay for their vignette - $15 for 10 days.