The fees charged by the NRC to applicants for an NRC license and to holders of NRC licenses and the associated requirements are found in 10 CFR Part 170 and 10 CFR Part 171. See in particular 10 CFR 170.20 and 170.21, and 10 CFR 171.15 and 171.17(a) for sections directly applicable to fees for nuclear power reactor licenses.
Nonprofit educational institutions are generally exempt from fees for research and test reactor licenses as provided in 10 CFR 170.11 and 10 CFR 171.11. Other research and test reactor applicants and licensees are subject to licensing, inspection, and annual fees. See in particular 10 CFR 170.20 and 170.21, and 10 CFR 171.15 for sections directly applicable to non-power reactors.