The situation is actually a bit of a grey area regarding insecure wireless networks, and probably depends on what country you're in - it's far from being classed as one way or the other for definite though.
It becomes a bit more clear cut on the illegal side when you break into networks (i.e. cracking WEP keys!) but I'll assume you're not going there!
If you got a wireless adapter though you can still connect to insecure wireless networks the same as if you had a laptop. It sounds like you want something new along the laptop / netbook line though anyway, and if this is the case then I'd recommend a netbook - they're small, cheap and perfect for browsing the internet or doing other everyday things