Greg,
My easiest/longer route for that flight is down past KCOS and R-2601 A/B, and then make a right to go West up the valley there over 1V6 and then follow the valley, the railroad tracks, and the river up to Salida. Piece o' cake. Just look over your charted obstacles and altitudes and keep track of where you are, and it's easy.
The other common way is to come down from Buena Vista, down-valley... and to get there is basically the reverse of how you typically get out of the Leadville area and back to Denver.
It's basically the route of V160 on the chart, maybe a bit south of that to cross over Wilkerson Pass in the vicinity of the Badger Mountain RCO (which is a very easy to spot landmark... lots of radio stuff up there for the State and Feds), and then you could either go West from there over Antero Reservoir (pretty from the air), and over the Trout Creek Pass area into Buena Vista -- then south down-valley, or really if you're willing to climb, you can get into the KAEJ/KANK valley from anywhere East of there (the depicted TERRO intersection route on the airway if you're high enough to receive Blue Mesa or using GPS, but there's no real need to be that high there). The issue is the further south you come once you leave the Badger Mountain RCO area, the higher the ridgeline is between you and the valley. The terrain is about 11'000 or so if you were to go "ridgeline direct" from Badger Mountain into KANK. It's not much better up at the north end, you'll still be pretty high.
Me, I don't like having to do the "slam dunk approach" that results from crossing that ridge and then having to get down to the airport when I can wander over Buena Vista and do a normal letdown coming down-valley there. And if the weather is weird over the Badger Mountain area, sometimes the valley up from PUB is wide open. Hard to find out from the ground in Denver, though.
Be sure to check out the A/FD remarks for the airport... the depicted "glider" on the VFR chart there on the ridgeline to the East is usually hang-gliders (noted in the A/FD) and they're tough to spot but usually brightly colored, at least. And they recommend 24 for arrival and 06 for departure, wind permitting. 24 can have sinkers on the approach in high winds, but going up there in high winds isn't super bright anyway... too bumpy.
Check out the missed approach on the RNAV GPS-A for KANK sometime... it's a fun one to show flat-landers. "Climb to 16,200' MSL..." Ask 'em if their airplane can do it.
Both KANK and KAEJ airports are down in the valley and not that "high" for us Denverites... (7523') but of course, always check temperature and density altitude...
And if you haven't done it already and want to take the time to do your DA calculations, etc... the "up the valley from the south" way into Leadville is a pretty easy way to get your "I landed at the highest public-use airport in the U.S." certficate... but I highly recommend doing the Colorado Pilot's Assn. Mountain Flying course first.
Flying something with over 200 HP, and coming into Leadville after climbing out of KASE, backtracking up the valley to Reudi Reservoir while climbing (and climbing and climbing and climbing) over Hagerman Pass... and then doing THAT "slam dunk" over Turquoise Lake is a far more interesting way to get to Leadville than up the valley from the South.