Indigo is absolutely right! When you say "Ich möchte beide." it would mean that the waiter has got two different cups in his hands already and you want exactly those two cups, while if you say "Ich möchte beides." you're just saying you want any two cups with coffee and tea.

Hm, "ich möchte beides" would be right in this situation. "Beide" names concrete things. If the waiter offered you two cups and you should choose, THEN you could say "ich möchte beide". Is this helpful...? Don't know.^^"

"beide" is short for "beide Tassen, beide Frauen, beide Kinder" etc. and is ALWAYS plural. "beides" is simply the abstract expression for "both". I hope that helps.

PS: just found two typos in my comment. It's supposed to be "...also müssen wir nicht weit gehen" and "...und erst nach Jahrzehnten wieder aufgebaut."

Maybe someone already answered your last question cause it's been quite a while since you asked. i'll try to answer it anyway ;) I thought about this quite a while and you're absolutely right "Rathaus" and "Kirche" are two very concrete things in the situation you described. But in the situation you described for the man who answered the question even though he knows the concrete buildings the lady was talking about they aren't quite "that concrete" because he's just very generally giving directions to something that's not right in front of him and he's not giving any specific information about the two buildings as distinct ...how to put it...entities? While thinking about your question i remembered how i once asked an american lady when to use "this" and "that". We were sitting at a table and kept pushing a coke can step by step further away from us and at a certain point she said "now it's that coke" and when i pulled it a little closer again it was "this coke" again. I think it might be a similar case with the question when to use "beides" and "beide". You know a tourist guide might pick you up at the central station and say "Wir schauen uns heute den Dom und das Rathaus an. Beides ist im Stadtzentrum, also müssen wir nicht gehen." and when you're standing right in front of the concrete building and he's giving you some concrete information about the two buildings he might say this "Der Dom ist im gotischen Stil, und das Rathaus im regional üblichen Stil erbaut worden. Im Krieg wurden beide zerstört und erst nach Jahrzehnten wirde aufgebaut." So i guess it takes quite some practice to estimate when something is concrete enough to use "beide" and when something is abstract enough to use "beides". It doesn't really change the meaning when you get it "wrong".