When I am choosing hotel [that I am not going to pay for out of my own pocket ;-)], free Internet access isn't what I look for. I am *much* more interested in free (or at least heavily discounted) access to "wellness centre"(*) or at least a sauna and swimming pool.
For entertainment, after I am finished with trying out all the goodies in wellness centre, a TV set with CNN, or, preferably Discovery Channel in English is enough. Of course, I never EVER travel without my trusty e-ink reader stocked with enough books. That is all I really need.
I can get enough Internet at home for very reasonable price
. On a business trip - 15 minutes in the lobby with notebook on my knees, or a borrowed Internet account at the office of our business partner is usually enough for me.
But ... I do not travel that much on business nowadays. And when I do travel, we usually only stay one night in one place and we only sleep in a hotel, so most of the time we simply select least expensive 3 star, or even 2 star hotel. When you check in in the evening and have to check out early in the morning it doesn't make much sense to get into posh hotel.
(*) wellness centre here in Europe usually means: several saunas, cooling pool, tepidarium, pool with massaging jets, jacuzzi pool, salt cave ... hours and hours of fun ;-)