Connecting to Different APs

At hotels, motels, airports, and many other sites I am unable to "associate" on many occasions. These sites are all infrastructure, no password, no WEP, no apparent, to me, reason why I should not be able to "associate." Some of these sites have strong signals, i.e., greater than 70 percent. At the same time time I am able to connect to some APs with very weak signals, for example, 20 percent signal strength. I use a LinkSys USB adapter which will connect almost when no signal is present. Could someone educate me as to the reason that I cannot connect to these very strong signals on the one hand, and can connect to very weak signals on the other hand?? Thanks