Gosh I've trekked from one of Kent to the other more times than I can count. Generally it's wealthy though with the odd run down town (by southern standards - nothing to compare to some of the run-down places I've been to up north). There are tons of train lines and stations and also ferries to France as well, though it still feel 'Kent-ish' if that makes sense, as opposed to say Surrey or Hertfordshire which just seem like extension of London.
Faversham is nice but very small and slightly 'villagey'. Not sure if that's what your after? Sittingbourne is nearby, more of bustle to it, though not the most exciting place.
Maidstone is ok - fairly nondescript place tbh like Basingstoke. Decent enough little town.
Ashford is quite similar just further out (though with a high speed rail link into London).
Of the Medway towns Rochester is easily the nicest.
Tonbridge, Canterbury, Sevenoaks - nice places, expensive.
Some of the coastal town in Kent are great - Ramsgate, Broadstairs, Herne Bay, Folkestone, Deal, Sandwich etc. A lot of DFLs (Down From Londoners) are moving there though so property price are rising all the time in whatever the latest 'trendy' place is (e.g. Margate).
Gravesend, Dover are likely cheaper but runs down in parts. Dover in particular is probably the worst town in Kent... such a depressing introduction to England for visitors.
Beyond that there are of course countless villages, most of them lovely, though generally expensive and of course much less going on and probably quite boring for teenagers.
Bear in mind also that most of south-east London was formerly Kent and many there still identify with the county. Bromley, Beckenham, Bexleyheath, Orpington etc. all decent places with a suburban feel though of course prices will be quite high given that your're in the M25.