Where are they? Interstellar Space more than likely, anyone FSDing around sol and surrounding stars has probably passed them in whichspace, the chances that you would be in a system when they arrive is very very small. It's not like they will be traveling slowly (0.7c-ish) they would have to expend a massive amount of energy to stop at any system, and they would need to be very sure they could either stay or have the resources available to refuel etc, to then begin to slowly punch up the speed again, (stopping in a generational ship will cost you a generation to get back on track).
If the crafts themselves have survived 1000 years without crashing/wearing out or have a social/crew issue, then statistically, without an exact leave date/heading/speed/flight plan, if they still survive, finding them in a system (because we skip the connecting space) is highly unlikely.
Even in the best case, they are traveling between systems 99.9999% of the time.
I always thought the purpose of a generation ship was to do a single voyage to a likely destination (based on astronomical observations) & then stop. If the observations are incorrect & the system's not habitable then they die, or survive using the ship as a base. So they would have set off for destinations not too far from Earth, e.g. Alpha Centauri, Pleiades, etc. So I would expect to find inhabited (by their descendants) systems &/or dead generation ships within a 1kly bubble from Earth. Many should have arrived by now (3302), but we haven't found any. Perhaps M erope 5C is a generation ship covered by galactic detritus & we're looking for the entrance hatch?