Unless he is a commercial pilot, then I don't think he can be reimbursed for expenses legally. Depending on the plane, for typical GA planes., it could burn 10-15 gallons per hour at $4-5/gallon. For my plane I figure fixed costs of $100 per hour...Cirrus SR22. Indeed, some airports charge a landing fee.
Kind of a wide open proposition without knowing details or capping expenses. Ask him for a detailed estimate of those expenses...a good flight plan should be able to establish that.
You can check fuel and landing fees online...
www.airnav.com as a start.