Can you file IFR to a location that only has an RNAV(GPS) approach? Yes. What about to an alternate that only has an RNAV(GPS) approach? Yes. What about to both? It depends. It depends on how well you are equipped and on if either of those locations has WAAS.
The prohibition against relying on a GPS approach at your alternate has changed, provided you, your airplane, and your destination meet a few requirements. The IFR world changed for us in April of 2013 when the FAA issued a Policy Statement announcing the change. The Aeronautical Information Manual now reflects this new philosophy.
Everything here is from the references shown below, with a few comments in an alternate color.
[Aeronautical Information Manual] ¶1-1-19.g.] Any required alternate airport must have an approved instrument approach procedure other than GPS that is anticipated to be operational and available at the estimated time of arrival, and which the aircraft is equipped to fly.
[Instrument Procedures Handbook, pg. 2-11] Not all airports can be used as alternate airports. An airport may not be qualified for alternate use if the airport NAVAID is unmonitored, is Global Positioning System (GPS) based, or if it does not have weather reporting capabilities. For an airport to be used as an alternate, the forecast weather at that airport must meet certain qualifications at the estimated time of arrival. Standard alternate minimums for a precision approach are a 600-foot ceiling and 2 SM visibility. For a non-precision approach, the minimums are an 800-foot ceiling and 2 SM visibility. Standard alternate minimums apply unless higher alternate minimums are listed for an airport.
[Aeronautical Information Manual, §1-1-17, ¶b.2.(5)]
(c) For flight planning purposes, TSO-C129() and TSO-C196()−equipped users (GPS users) whose navigation systems have fault detection and exclusion (FDE) capability, who perform a preflight RAIM prediction for the approach integrity at the airport where the RNAV (GPS) approach will be flown, and have proper knowledge and any required training and/or approval to conduct a GPS-based IAP, may file based on a GPS−based IAP at either the destination or the alternate airport, but not at both locations. At the alternate airport, pilots may plan for:
(1) Lateral navigation (LNAV) or circling minimum descent altitude (MDA);
(2) LNAV/vertical navigation (LNAV/ VNAV) DA, if equipped with and using approved barometric vertical navigation (baro-VNAV) equipment;
(3) RNP 0.3 DA on an RNAV (RNP) IAP, if they are specifically authorized users using approved baro-VNAV equipment and the pilot has verified required navigation performance (RNP) availability through an approved prediction program.
(d) If the above conditions cannot be met, any required alternate airport must have an approved instrument approach procedure other than GPS−based that is anticipated to be operational and available at the estimated time of arrival, and which the aircraft is equipped to fly.
[AIM, §1-1-18, ¶c.9.(a)] Pilots with WAAS receivers may flight plan to use any instrument approach procedure authorized for use with their WAAS avionics as the planned approach at a required alternate, with the following restrictions. When using WAAS at an alternate airport, flight planning must be based on flying the RNAV (GPS) LNAV or circling minima line, or minima on a GPS approach procedure, or conventional approach procedure with “or GPS” in the title. Code of Federal Regulation (CFR) Part 91 non−precision weather requirements must be used for planning. Upon arrival at an alternate, when the WAAS navigation system indicates that LNAV/VNAV or LPV service is available, then vertical guidance may be used to complete the approach using the displayed level of service.
Of course this doesn't say you can file to both the destination and alternate when relying exclusively on GPS-based approaches, only that you can at the alternate. We already know we can at the destination. Helpufully, the FAA also issued a Policy Statement with a specific example that ends all debate:
[FAA Policy Statement, Policy Clarification Example]
Aeronautical Information Manual
FAA Alternate Airport Flight Planning Using GPS and WAAS Policy Statement, Effective 4/04/13 to 5/01/13
FAA-H-8261-1, Instrument Procedures Handbook, U.S. Department of Transportation, Flight Standards Branch, 2004
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