I personally wouldn't try to visit any of your locations as a day-trip as you'll likely be spending more time traveling than the actual location. At best, it will take 3+ hours one-way to reach Paris, Amsterdam or Switzerland via train (I'm assuming that is how you plan to travel). I would either allocate more time to seeing another country in Europe or visit places in Germany that are closer. There are many day-trips that one can take from Frankfurt that are discussed on this forum including a trip down the Rhine River. You could also visit Strasbourg, France with a 2 hour train ride if you really want to visit another country.

You should spend some time on DB site (German train schedule) http://www.bahn.com/i/view/index.shtml to see exactly where you can go with your schedule. It will also depend upon connections and the type of train, some routes are faster than others even if they are further away.

Yes, I plan to travel by Train. I will check out Strasbourg, France. Thanks for that.

I really do want to visit other countries as this is my first time in Europe. What other cities or countries can you you suggest are close to visit aside from Strasbourg, France? I am checking our DB Bahn and Eurail now.

I think that in order to provide you with recommendations we would need to know, what is the maximum time that you're willing to travel to reach a destination? What are your interests? What do you really want to see? For example, if you said I've wanted to see Paris all my life and this is my only chance, then I'd say go for it but in almost any scenario, you're going to spend a lot of time traveling to reach another country. Is that worth it to you to say you've been there? If yes, then you could certainly go to Paris or Amsterdam.

My maximum travel time would be 4 hrs one way. I want to visit the iconic cities/landmarks in Europe. I am not sure when I could go back to Europe again so I would like to maximise the time that I will be in Frankfurt to visit as much countries as I can.

4 hrs one way is to much time spent on the rail and wont take you far.

You could reach Paris in just under 4 hours if you take the direct TGV. The same for Amsterdam with a direct ICE train. Those would be my picks for iconic Europe.

Have you considered going by plane instead? There are lots of relatively cheap airlines that go all over Europe -- not sure if you save any time given the airport hassles though. Might be worth checking out.

Perhaps the Netherlands, Belgium or Luxumbourg?

For most of the cheap airlines she would have to go to Hahn, eating up time again.

You could consider Belgium or Luxemburg, Paris and Amsterdam, but what kind of day trip is it if you spend 8 hours on a train to get there and back, how much time do you have left to see anything?

Ok, if you want to spend the 8 hours on the train just to see the Eiffel tower and Notre Dame, but I still think you should spend the night in Paris then.

You could check into cheap flights, but that would mean an over night too, Frankfurt is pretty central, but that means to get to a border takes it's time.

In Ocotber the Rhine and Mosel valley will be lovely and very convinient for a day trip, Franken also wine country can be reached in a short time, the vinejards will have Straussen Stuben set up to taste wine.

If you want to leave Germany you have to plan in an overnight, except Amsterdam or Luxemburg, Belgium, why not explore Germany a little deeper?