Hi majkportnoj

I can't speak much for Bern and I can say little about Bienne, but I'll try and help if I can. Bern might be a little more central for you if you have to travel all over the place but I'm sure you've already seen that on a map! The train infrastructure is excellent, I can't speak for Hungary but comparing it to the UK is like moving from a square wheel to a round one...

For creche, kindergarten or finding people to look after kids it seems the earlier you are on a list the better, we have personally found child care difficult to come by, but some are luckier than others.

Furnished apartments must exist but I've heard they are rare, try www.immostreet.ch, www.immoscout24.ch, www.annonz.ch or similar sites

Good luck, I hope it all works out well for you...