Do many Class E/G airfields charge for short stops without gas purchase? Sorry for the stupid question...recent PPL here and my training has mostly been T&G rather than full stops to the FBO. Planning a XC to KSHD and wanted to stop in for a bit to check out the facility.
I have found this really varies by airport and even by FBO at a given airport. The only way to know is either to check their website or call in advance and find out. After a quick look I don't see any prices listed on their site.
Often times the price is related to the services they provide by default. If you land and there is a marshaler waiting for you, a golf cart ride from your spot to the FBO building and loads of free local snacks: you're likely to be paying. If you land and the airport manager lives next door but his cell phone number is written on a sign that says "call for assistance", the fuel is self serve, and the gate code is the CTAF frequency: you're likely not paying for parking.
The one thing that's worth noting is if there is a local (usually nominal) landing fee charged by the municipality the airport resides in.
AOPA's airport information site has some fee info on it. For example KLOM has some fairly high fees for a class E un-towered field. While I can confirm from experience that the $5 ramp/parking fee at KDDH is waved for buying fuel.