How about homing in on a type of bike you like, then fit that in to your budget?
$4K could buy you a nice bike, no doubt about it.
Since scouring the classifieds is one of my unhealthy obsessions, I'd say you're best bets for a clean, hopefully problem-free ride would be a mid-'90s sportbike:
Suzuki SV650 -if you shop around, this can be had for $4K
Kawi ZX6 d/e (Not the "R")
Yamaha FZR600 (maybe a YZF600R but those usually gor for $5K)
Honda CBR600 f2/f3
Honda VFR '92-'93 ('94-'97 if you are very lucky)
best bike is very relative. i would say a 98 zx9r would be one choice.
are you new to riding?
if so, i would spend closer to 3k to get something that runs good and still have plenty of dough to buy gear with. 3k can get you more than enough newbie machine. i'd suggest finding a gpz550 and keeping 3k in you pocket. it'll make a great downpayment on a newer bike next year. and you can sell the gpz for more than you paid for it if you can negotiate well.
been riding awhile. $4000 would snag a kickass air-cooled gsx-r1100. or a real nice air-cooled gsx-r750 (or semi-nice gsx-r750 limited edition). maybe a 93 zx7. or how about an fzr1000. monster motor, comfy. or a zx10 and an ex500. a twisties slaying ex500 and a go to work, go to 170 zx10....hmmm nice combo.
you can get a 93 cbr900rr that needs some help. or a ducati 900cr (maybe a real headache at that price). of course there's the possibility of a worked honda hawk 650. or a mediocre yzf750.
hell, some specials should be coming in at that price. gsx-r7/11's (a personal favorite). or an fzr400/600 (for 4k, the motor better be worked and it should have a different front-end and 17" wheel).
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