Well I nominate Salt Lake City first because it is the link between Central Pacific's and Union Pacific's ends of the Original American Transcontinental Railroad (Not exact, its at Promontory Summit 66 miles to the NW of Salt Lake, but its still within driving distance and would be sight you'd never forget.). They still recreate the driving of the golden spike there as well, bringing out replica's of Central Pacific's #60 and Union Pacific's #119 steam locomotives to recreate it.
Cheyenne, WY is home to the UP steam program and has a still operating round-house. Plus it of course is on the UP Transcon, so you can expect to see tons and tons of freight trains crossing Sherman Hill. Sherman Hill where the Transcon crosses the Continental Divide at an elevation of 7,960ft.
Portland, OR is home to 2 UP yards, and 2 UP intermodal terminals. Plus Trains going from Seattle, WA always have to pass through Portland to get east. Plus there's also a BNSF yard in Portland and quite a few BNSF Trains roll through. And if you're a scenic person, then the wonderful sights of Mt Hood, and the Columbia River Gorge (With UP and BNSF tracks on each side of the river) are a must visit location!
As a railfan, you couldn't possibly visit Oregon without paying a visit to the Blue Mountains line (Consist of both the UP Hunnington Sub and UP La Grande Sub) La Grande just happens to be situated between the major points of Nampa, ID and Hinkle Yard just outside of Hermiston, OR. It is the helper (Still is too) district between both the 2% Grades going east or west. Plenty of trains traverse this line. It's situated in of course, the Blues Mountains District, along with the Baker Valley, and my favorite, the Snake River valley. Splendid sights out there, been there several times. Love it each and every time!
Pocatello, ID is home to probably Idaho's largest yard, the Pocatello Yard. It's situated on a link that comes north out of SLC and rolls east from there linking Portland, and Seattle to the rest of the eastern cities. A branch line extends off to what used to be a UP link to the north and small transfer yard at Idaho Falls, ID. Plenty of good freights traverse this line as well. If you like traveling from state-to-state, then you'll want to follow the UP Pocatello Sub a little further South and West where there is the crossing of the Snake River over the American Falls Dam. You can then follow the line out to Minidoka, ID where there is an old UP steam days water tower. Plus there is a small interchange where cars will sometimes go over to the Eastern Idaho Railroad, A class 3 covering from of course, Minidoka, ID over to Twin Falls, ID. If you love that old power, then the EIRR is your dream. They have a fleet of classic EMD locomotives, including GP30's, GP35's, GP38's, GP40's, and even GP50's. If you continue to follow the UP line out of Minidoka, it transitions into the UP Nampa Subdivision. The beautiful Idaho Sawtooth Mountains are often visible from the line, and if you go in spring or fall, they are snow capped while the ground in the valley is yellow, adding to the natural beauty of the line. If you're a friendly crew fan, I've been covering this line now for about 14-15 years, and I've only gotten one middle finger. All the other times, waves and hornshows. Bliss, ID through to Reverse Grade (aka Medbury Hill) are wonderful spots nestled along the Snake River Gorge in South Central Idaho. You'll find that a lot of relics of the steam days remain. They have the water towers, the phone booths where the crews would call in if they had an issue, and many of the telegraph lines still remain.
North Platte, NE of course is home to the largest railyard in the world. Bailey's yard takes up an area of about 8 square miles. Where else can you see over 100 trains a day flash past? And of course, they have North Platte Railfest every year, bringing in the UP steam, the E9's, 6936 the last remaining operational DD40AX, and the UP Heritage Units (UP 1996, 1995, 1989, 1988, 1983, and 1982). At Baliey, you can see up to 8 trains at one time being refuled, 11 1+ mile long trains could be on lay over at any given time. Its insane.
I know this post is a bit biased towards UP, but UP is America's oldest Class 1 at 152 years old and I love the UP railway. I have so many memories with them. So I say if you want memories, visit anything to do with the Union Pacific Railway
