You will be able to book for that length of time if booking your accommodation separately i.e not as a package deal.
My advice would be to look up flights that suit (but don't book at that point), then look at all the accommodation websites (travel republic, alpharooms, thomas cook, thomson etc) and see if you can find accommodation to match the flight dates.
I've spent longer than that in one area of Menorca in the summer and not felt that it was too long at all. I guess it depends what you want out of your holiday. Some people are happy just to kick back and take life at a slower pace and what better place to do that?!
As for recommendations, I think that depends a lot on your budget and criteria. Perhaps staying that length of time you're looking for a comfortable/luxurious base with everything you need, or perhaps your'e trying to get something as cheap as possible in order to stretch to 3 weeks?
The best priced aparthotels seem to be coming up around the Cala Blanca area on the sites mentioned above. Not a bad base as you can easily get to and from Ciutadella and to the other west coast resorts with a regular bus service (or a lovely long coastal walk!).
Good luck, I hope you find something to suit.