Match tickets for Euro 2024 will include free travel on public transport for 36 hours, from 6am on matchday until 6pm the day after. That will be for travel anywhere within the regional transport network in which the host city is located. That means you could stay out of town and still travel to and from the game for free. So, it'll be useful to know which towns are covered by each network. That's what I've listed here (along with direct links to the Booking.com hotels page for each of those out-of-town locations).

Hamburger Verkehrsverbund - HVV (host city: Hamburg)
HVV network map
One of the smaller transport networks offering the 36 hours of free travel. Includes Itzehoe, Stade, Buxtehude, Soltau, Lüneburg, Dannenberg, Büchen, and Bad Oldesloe.

Verkehrsverbund Berlin-Brandenburg - VBB (host city: Berlin)
VBB network map
Out-of-town locations covered include: Angermünde, Nauen, Rathenow, Brandenurg, Potsdam, Bad Belzig, Jüterbog, Elsterwerda, Cottbus, and Frankfurt (Oder).

Mitteldeutscher Verkehrsverbund - MDV (host city: Leipzig)
MDV network map
Includes Halle, Dessau, Naumburg, Altenburg, Colditz, Döbeln, Oschatz, Torgau, and Lutherstadt Wittenberg.

Rhein-Main-Verkehrsverbund - RMV (host city: Frankfurt)
RMV network map
Includes: Marburg, Dillenburg, Limburg, Wiesbaden, Mainz, Bingen, Worms, Darmstadt, Aschaffenburg, Offenbach, Hanau, and Fulda.

Verkehrs- und Tarifverbund Stuttgart - VVS (host city:Stuttgart)
VVS network map
Like Hamburg, a relatively small network that doesn't extend much beyond 'Greater Stuttgart'. Includes: Marbach, Ludwigsburg, Bietigheim-Bissingen, Weil der Stadt, Böblingen, Filderstadt, Neidlingen, Ostfildern, Kirchheim, Schorndorf, and Backnang.

Münchner Verkehrs- und Tarifverbund - MVV (host city: Munich)
MVV network map
Mainly just 'Greater Munich'. Includes: Freising, Petershausen, Herrsching, Tutzing, Wolfratshausen, Holzkirchen, Ebersberg, and Erding.

Verkehrsverbund Rhein-Sieg - VRS (host city: Cologne)
VRS network map
Includes Leverkusen, Kerpen, Erftstadt, Dahlem, Euskirchen, Bonn, Königswinter, Windeck, and Marienhelde.

Verkehrsverbund Rhein-Ruhr - VRR (host cities: Dortmund, Gelsenkirchen and Düsseldorf).
VRR network map
The big one! Includes: Bochum, Herne, Mönchengladbach, Oberhausen, Solingen, Bottrop, Duisburg, Essen, Hagen, Krefeld, Mülheim an der Ruhr, Remscheid, Wuppertal, Kleve, Recklinghausen and Wesel.

NB: These last two networks are operating as one for the purposes of match ticket validity during the Euros. So, for example, if you have a ticket for a game in Cologne (the VRS network) it will be valid also for travel to/from towns in the VRR region.

For some suggestions of places to stay in the host cities themselves, go to the respective page under Venues and for links to hotels on the dates that each city is hosting a match see my Dates page.