All Courtyard by Marriott are supposed to have WIFI (Wireless Fidelity, 802.11 wireless, 11mb/sec wireless, however, their upstream link may only be a 1mb/sec) or hardline access to the net. Bass Hotels and Holiday Inn/Holiday Inn Express are also supposed to have internet access. Wyndham has done most of their facilities with HotelNet.
Problems you might run into:
Email will need to go via a port OTHER than 25/SMTP if you want to use your own mailserver
Sometimes SSH will not work outbound because of their proxy-nat. FTP & Web Surfing usually works with no issues. FTP will probably require passive mode.
If you're going to depend on hotels, check to make sure that the Hotel chain works in one city -- then it is most likely to work in their other cities.
There's always T-mobile and their WIFI network at McDonalds, Starbucks, etc
http://tmobile.com/hotspot/default.a...&WT.mc_t=Other
As for using a laptop as a machine, you might consider what they call a DTR - Desktop Replacement. You might find some of the ones with longer battery life to be too slow or too compact for what you need it for. I've used a laptop as my primary machine since '93 or so and I would NEVER use a desktop again. Generally, I'll get about 3 years of life out of them and I don't really treat my laptops gently.
If you are going to be in 'civilized' areas, Cingular has their Edge service which offers up to 200kb/sec on their network. If you're going to be on Sprint/Nextel's network, you can use their phones for a 19.2 digital dialup. Sprint has mentioned an Edge service as well, but, I haven't read much on it. GPRS3 was being deployed by AT&T/GSM prior to them getting purchased by Cingular. Some areas have it in beta where it offers 300kb/sec. GPRS3 has the ability to support multi-megabits per second.
Verizon offers
VZAccess which has reasonably good coverage and 300kb/sec down with 64-300kb/sec up depending on facilities.
Basically, the closer you are to civilization, the more likely you are to get higher speed connections. If you're going to stay in resort towns, I doubt you would have much problem finding connections.
You might check with some of the motorhome/motorcoach clubs like 'Good Sams'. Since people live on the road, they have probably run into the same issue and might have recommendations, discounts, etc.