I have an old 350 and it will cruise all day at 60mph. However, it won't do much more than that (maybe 70mph on a flat road) and my weight is an average 12 stone.
It is quite capable for commuting and keeps up with traffic. Having said that it would not be my first choice for getting to work and coping with traffic jams, filtering and half asleep car drivers.
Mad Mike maybe right in suggesting a Triumph but better value can be had if you are not fussy about it being a retro looking modern bike. If your budget is 2K it would probably not buy you a used Triumph, it would buy you a neat CB500 which frankly is the ideal tool for the job.
In fact, 1K would get you a CB500 with 1K leftover to buy an old Enfield for a leisure/hobby bike.
Cheers
Paul.
www.greenlane.biz