I agree with the others above... the SV650 or a lightweight supermoto bike are
a lot of fun for the money. A really nice used SV650 can be had for around $4k.
Used SM's are all over the map, pricewise, but I tend to like the deals where
the guy bought it and never really used it, which are more common than you
might think with _any_ kind of bike or rec. vehicle. The one negative of big
singles is vibrations. I like the big-inch KTM's but they do vibrate quite a bit
(other than the newer KTM 690 engine models which are not commonly traded
under $5k). Supermotos are the new commuter bikes! Try one and see. Not so
good for overnighters but you can put a bag on the Hyper for that.
As PedroHM mentioned, you will learn more/faster on a lightweight, flickable bike
than on a more intimidating lump of big iron. Supermoto bikes are designed to
be dropped and picked back up... your day isn't over if you drop one, especially
wearing good gear. Learning new techniques involves taking a certain amount
of risk, and dirtbikes don't discourage that behaviour to the degree a pricey
Italian steed can tend to discourage it.
The street cornering ability of
a Supermoto is astounding.