Neil - There are many aircraft that would meet your needs. An expert in the business would have the best information on range/payload capabilities regarding their fleet. However, looking at the least expensive aircraft to meet your reqs of four pax and flights up to approximately five hours brings several aircraft to mind.
Smaller aircraft that carry up to seven pax for shorter legs or your family for longer legs I would look into late model Leers...specifically, model 45 or higher in numerics. Some of the recent small Cessna Citations would fit well and directly compete with the Leers. Personally, I like the Leers better and they have excellent performance capabilities for the high PA (pressure altitude) locations (Jackson Hole).
If you wanted some flexibility to carry a slightly larger crowd upwards of ten-twelve people, perhaps for entertaining or business then your best options would likely be an older Gulfstream 3 series (G3). Similar in size, range and cost point would be the Hawkkers. With both of these aircraft you'll want to look into older aircraft as the latest varieties are extremely expensive (i.e. G5, G550, et al). These aircraft will also have cabin attendants where as the smaller will not. Basically, a crew of three vs just two pilots and inflight meal service is possible where as in the smaller aircraft it will not be.
During due diligence you'll want to know about a few pieces of avionics and certifications that are imperative for your cost and safety. If you fly into mountainous terrain areas you'll want to know if the aircraft is equipped w/ EGPWS (enhanced ground proximity warning system). In the early 90s we/USAF had a C130 crash into a ridge departing Jackson Hole at night. Had they had this system they likely would have survived and climbed above the rising ridge. Trust me that it is important for any location w/ rapidly rising terrain around it and the older system of regular GPWS does not cut it (the difference is in a feed of position via GPS compared to a database that correlates to aircraft altitude and flight projectory and displayed on a screen with visual/aural warnings for the crew). Next, you'll want to ensure that the aircraft is equipped w/ GPS and is RNAV capable (route navigation performance specifications). This allows the aircraft to fly virtually direct legs between airports vs overflying ground based navigational aids...this saves you money because you'll get there sooner as the distance to travel is shorter. Lastly, the aircraft needs to be RVSM (reduced vertical separation minima) certified. The class A airspace (18,000'-FL600) above the CONUS used to be broken down such that aircraft in opposite directions had 2000' of separation. With the introduction of RVSM that has been reduced to 1000'. Only aircraft that are RVSM certified are allowed to fly between FLs (flight levels) 290-410 inclussive. Four points here...fewer deviations are required at higher altitudes for bad weather (thunderstorms), the ride is much smoother (less turb), the aircraft will typically fly faster (less time enroute = $) and fuel effifciency is much better the higher you can get w/ jet engines even though you are flying faster. Most of the jets that you will consider will have ceilings of FL410-450. However, even to transit the RVSM airpsace you must be certified unless they can clear traffic out of your way which is nearly impossible anywhere east of the Mississippi River. To note, that altitude block will expand over time to include all altitudes between 18,000 & FL600. Thus, lower altitude = slower, rougher, longer and more costly to you.
There are many great aircraft out there for various needs. Don't let the age of an aircraft spook you, they are not like cars. A 20-30 year old aircraft could and should be as good as new. Engines, airframes and avionics undergo routine and mandated inspections and overhauls on a regular basis as mandated by the FAA.
Let me know if I can help guide you any further.
Ted
