Much easier/cheaper to go to the US if you want to fly into "big" (i.e. busy) airports. You'll be welcome at almost any airport in the country in just about anything which can fly, with no prior warning at all, and very rarely any landing fees
As for UK/Europe, if you want to mix it with the big stuff, have a look at RyanAir's routes - they tend to fly into airports which don't charge massive landing fees, and if they don't have to pay massive landing fees for their B737s then the chances are that landing your PA28 there will be almost affordable too.
FFF
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