Oh lordie. I love the first game oh so much, and because I love it, I have dreamt of many and sundry changes for the next iteration. It has so much potential, and believe it or not, it doesn't have to be online, although that would help, I admit. Let's look at some.
1) Online trading/train visiting. This could be very, very, very simple, like just having the ability to establish an internet connection to trade things. I'm not really all that interested in some kind of MMORPG type thing, because I get so sick of dealing with people being jackasses online, and the first guy who trampled my flowers would find themselves getting a real scolding! Still, online train visits would be supremely awesome. But it'd be cool if they only let you visit every so often so that you weren't abusing it.
2) More hobbies/recreations. I want to see more people doing more things in the town. Bonfires with marshmallow and frankfurter roasting, sideshows, perhaps small circuses or carnivals (in the right scope, that is; nothing big), more work opportunities like, let's say, item delivery (JUST KIDDING! Hahaha...), gardening, running mini-games, etc.
3) FASTER MENUS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! FOR GOD'S SAKE!!!!!!!!!!!!!!!!!!!!!!!!!! OHHH LORD! *weeps* Just a HINT OF INTUITION would help. Just a HINT. I love this game so much, and the more you play it, the more you hate parts of it. The menus are NUMBER ONE. "Hello there! *pause pause pause* What can I do for you? *pause pause* *make selection* Oh, is that all? *pause pause pause * [Long goodbye spiel]." EVERY TIME!!!!! *weep*
4) When there're things going on like games at the town fountain, I expect to PARTAKE IN THEM. I refuse to stand by while everyone plays tug-o-war and I can't. That's really disappointing, and it really makes you reflect on what exactly you're doing with your life. And I don't want that.
5) Did I mention better, less talky, menus?

6) Of course more NES games, but that seems to be the overwhelming plea at this thread.
7) Allow to carry more items and to organize FASTER, EASIER, and BETTER. This is a HUGE deal.

Nintendofy it. I just basically want them to pour that special Nintendo magic all over it and blow away all the ideas we can come up with. It's 2am and I'm going to bed.