I can't give you specific recomendations for resturaounts in basel, but what you want to have is Raclette - basically they bring a chunk of cheese in a special appliance to your table that melts the end of the cheese, and you scrape it off and eat it on a piece of cheese. this is more common in that part of Switzerland. a meal would be some bread and 2 or 3 types of hot cheese, and a plate of small boiled potatos to dip the cheese, and maybe a plate of air dried beef.
in switzerland in general, cheese is a good way to go - fondues and variations on fondues. also game can be very good. If you decide to go to Zurich let me know, I can scrape up a couple of specific resteraunt recomendations for you.
if you get to Zurich, go to the central train station and then walk down banhof strasse to the lake. there is a very nice cafe called Sprungli, which is very old school - the waitresses wear startched uniforms and the cakes and cookies are fantastic. in the station there is also a farmers market on saturday morning, with a wide variety of cheese and preserved meats, as well as sweets and honies.
Alsace has some great foods - it is a very distinct cuisine from the rest of french and german. one of the specialities is a platter of meats on top of sourkraut, there are also a variety of quishe type pies that are excellent.
in terms of travel - taking the train from switzerland to milan is spectacular - you go through the swiss mountains. but if you are set on going north, you can get a train to Berlin, too. the night train is a very comfortable way to travel, I have done it many times. you can actually get a very good meal on the train, if you travel first class (you need to pay for the meal seperatly, you eat in the dinning car).
in Berlin, there are a huge range of food options. I'd suggest cafe Einstine (which is both a small resteraunt chain and a cafe chain) on unter-den -linten in the east side. very good traditional austrian food. what germans would consider comfort food. also, get a donner - which is like a gyro, but it is real german street food, you can get very good ones around the zoo train station. Kant str. has a lot of the ethnic restraunts in berlin, there is a great ethnic population in berlin going back decades, and german chinese or turhish food will be different from anything that you have ever had.
aside from the food, berlin has some of the best art in the world, see the pergoman museum and the egypt museum.