A little more info on your likes & dislikes might be helpful for others to suggest good choices. Do you have to stick with Triumph or are you open to other brands, street, dual sport, dirt, luggage, windscreen, naked, used, new, etc.
There are 1000s of good choices out there, but I know BMWs better than any other brand, I would suggest from various categories:
vintage: any of the old airheads are great machines, easy to work on and rock solid reliable. Also a hoot to ride and get more attention than most newer bikes of any brand.
cruiser: R1200C -- made from 1998 to 2004 / it's a cruiser that handles like a ST bike and turns heads everywhere you go. I'm on my second one as the first one was totaled in Aug. '04. I have drven the two combined about 160K trouble free miles.
ST: the R1100RT -- made from 1996 to 2001 / named #1 sport-touring bike 4 years in a row ('98 to '01) it's not any worse of a bike now than it was then but technology has moved on and some think the new RTs are better -- I wonder though.
sport: R1100/1150S -- a buddy of mine owned one of the 1100s. later he had an RC51, a Busa, and a Ducati. He contends that even though the others were faster, the 1100S would out corner all of them. I can't attest to that as I never rode any of them.
K1200RS or K1200S; both screamin' machines.
naked: R1200R -- the newer ones have tons of power and lightweight to boot. Have another buddy with one of these. He is somewhat of a performance junkie and says it is the most fun he has ever had on a bike.
New touring: K1600GT -- great styling, great power, great handling. Reliability? The jury is still out.
I'm pretty sold on the boxer engines for reliability and ease of maintenance, but many contend the K bikes are better perfromers.
edit: oops, I just picked up on your budget requirements at 3 to 4K. Many of the oil-heads suggested will fall in that range along with older K bikes, but the newer ones won't.
cruisin Tx -- mostly between the fence rows
'85 250 Rebel
'86 450 Rebel
Last edited by cruisin; 11-22-2012 at 08:59 AM.
Reason: occasional brain death