Yes I have a similar problem. My old phone an HTC hero works all round the house on both mobile network and wifi. The mobile network also works around town and is usually quite quick.
The nexus galaxy connection seem to start, stop and stall I have performed several tests switching the sim card between phones and this is no exaggeration the HTC hero is ten times more reliable downloading data from wifi and the mobile network (GPRS).
Looks like this Nexus Galaxy will be returned in the next few days. It's a shame because other than that it is a great phone - but unfortunately connectivity is more important than anything else on smart phone as far I am concerned.
Signal strength on this phone seems to be sucky in general.
I picked up my Verizon LTE GN yesterday and have had signal issues with it.
With my Droid X I would get 3 bars of 3G at my house. The GN only gets one.
With my Droid X I could be on my hammock in my backyard, about 20 yards and a couple walls away from my router inside, and I'd have like 50% wifi strength. With my GN I lose wifi connection 20 ft from the router, and that's inside the house.
Isn't there a setting to not have the Wi-Fi radio at full power?
I know some phones have that. On those, it's not at full power by default.
I know it seems odd, but I'm guessing it's a battery saving feature.