There are 4 days in our 3 week itinerary where we are in the city for only a day (no overnight stay) & hence we are not checking in a hotel. Do the train stations let you check in your bags for a fee? We are a couple & are carrying 1 bag pack each. These are the cities where we need to check-in bags - Frankfurt, Florence, Pisa & Budapest Thank you in advance!
Frankfurt main train station, (Hauptbahnhof) has lockers that cost 5 euro. They are located next to track 23. You will need coins for these. They also have a luggage storage facility, that charges more per bag, but they aren't open all the time, nor on Sunday at all.
In Florence, the Santa Maria Novella station (the main station) has a luggage depository, in Pisa the Centrale station has one. Allow sufficient time to pick up your bags before your train - there is usually only one attendant and he might be on a break or there may be a couple of people ahead of you.
The Bahn has information, including a map, about the Franfkurt Hbf at http://www.bahnhof.de/index.html?lang=de#station/18215 Click "Service rund ums Reisen", then "Gepäck". According to DB, the least expensive lockers (small 3,50€, large 5,00€) are next to Gleis (track) 24 and at the exit to the Vorplatz, opposite tracks 18/19. In my experience, a small locker has held two regulation carry-ons with room to spare, maybe enough for a third. The lockers only take coins. Be sure to have exact change; no change is given. The Handgepäckaufbewahrung (check room), in the main hall, opposite the DB Reisezentrum (Travel Center ) is open 6:30 AM to 7:30 PM weekdays, closed Sat/Sun.
Do you know if you're arriving and departing from the same station in Budapest?
When you say "check in" your bag, I'm wondering if you might have a different idea. Everyone here is describing options for stowing your bag while you're touring during the day. Trains don't check in bags like an airplane (at least not on any train I've ever ridden). You need to lug your bags on and off the train (another great reason to pack light). Many, but not all, stations have lockers that you pay to use. Some, have a left luggage office that is essentially the same thing, while others don't offer any service. I think all the one's you are visiting will have lockers.