The words 'larger airports' and 'cheap' do not sit easily together, nor does 'avoid handling fees' .
By 'larger airports' do you mean busier airports, or airports with huge runways and no traffic? ISTR someone taking a PA-28 into Gatwick recently, it was quite painless, only cost about £800.
Its probably more challenging to get into a small airport with a high volume of traffic than a large airport with low numbers of traffic.