I stayed three nights at the Izaak Walton last June with my father. We stayed in one of the first floor "Great Northern" rooms.
On the whole, this is a wonderful place to plan a stopover...with one caveat. This historic inn is not "handicap-friendly". They have installed a chair lift so that handicapped patrons can enter the first floor restaurant and rooms, but the bar/lounge and TV room in the basement are not accessible. If I recall correctly they have one unisex accessible restroom on that first floor, but I do not know if any of the sleeping rooms have been modified to be ADA compliant. Also not sure about transportation for wheelchair guests from the Amtrak platform, which is about 1/4 mile up the tracks on a gravel road. The hotel sends its van to meet all guests arriving by Amtrak, but I don't recall the van having a chair lift.
If you don't have that particular difficulty, though, the Inn is a wonderful and relaxing place to spend a few days. It does have a full service restaurant serving breakfast, lunch, and dinner; there is a bar and lounge downstairs (be sure to take plenty of dimes or half dollars for the antique jukebox...quarters don't work, but dimes do!) as well as a TV room (there are no TVs in the rooms) and game room; there is a small laundromat across the parking lot if you need to wash clothes, plus those wonderful huge porches on both the track side and the parking lot side...a great place to sit and relax and watch some BNSF action! Some of the "rooms" are cabooses or locomotives which have been converted into cabins, and I believe that there are a couple more across the tracks...there is an overhead walkway which lets you cross the tracks without hazard, and it too is a great place to watch some "action".
Some of the Red Bus tours (the Circle tour in particular) do stop at the Inn and they are a great way to see the park proper. (The Inn is actually just outside the perimeter of the national park.) Even if you visit in late spring or fall when the Circle tour is not offered, try giving Glacier Park Inc. (the Red Bus concessionaire) a call anyway and tell them you're staying at the Izaak Walton...they may be willing to pick you up for one of their other tours for an extra $10 a head or so. (You're 30 miles from the park entrance over 2-lane roads...it's worth it!) We took the Old North Trail tour and had a wonderful time...our "jammer" guide was extremely knowledgeable and personable. Tip accordingly!
Some things to keep in mind: The hotel rooms do not have TV (some of the cabins may), but there is a comfortable TV lounge in the basement. The hotel requests no laptop or electronic devices usage in the main lobby (a wonderful public space with comfortable chairs, hundreds of books, and an inviting fireplace), but you may use them downstairs in the bar where there is wi-fi. (Our connection speed was slow, but that may have been due to bad weather...I think they use a satellite link.) There is no cell phone service within 30 miles, but pay phones are available and the front desk sells phone cards.
I have heard that it may be possible to arrange auto rentals with advance notice; check with the hotel office for more information. (We drove our own car.) Activities in the immediate vicinity are limited although there are at least two decent eateries if you want a change of pace from the hotel restaurant; for more choices and activities you will need to drive the 30 miles to East Glacier or West Glacier (the Inn is almost exactly midway between the two park entrances).
The Inn as seen from the pedestrian bridge over the BNSF tracks. Please note that there are no grade crossings on the main line anywhere near the Inn, so whistle noises are seldom heard, and the Inn is set far enough back from the main line that the train noise stays well into the background.
The Flagstop Bar in the basement. You can use wi-fi here whether the bar is open or closed.
The antique jukebox (there's a modern CD jukebox at the far end of the room as well). Bring plenty of half dollars or dimes!
One of the Great Northern guest rooms on the first floor, with queen and twin beds.
We had a great time at the Izaak Walton, and I would love to return there some day...hopefully via Amtrak!
Very nice little Diner in the Inn it's self. The inn has a shuttle from the Gravel yes Gravel platform marked with two or three lampposts and IIRC a switch box. Type of thing you will walk right by it when walking. I would most surely recommend it! It's a very rail fan friendly hotel! Trains often blow there horns as they pass. There is a overpass that crosses into a caboose yard. That is the staff's housing. Don't expect to get Cell Phone or Internet Service there. Just a pay phone. The station as mentioned is gravel you can walk and takes less then 5 minutes and about 2 minutes by the hotel shuttle, if that. Their are track side rooms. Book well in advance for those! Make sure to book a jammer tour through the park. It takes up the whole day and is a blast! If you choose to stay there I'd say two days including the day you arrive if your coming eastbound on the EB. One for train watching! The other for the tour. Then if your going onto CHI like we did woke up next morning had breakfast and they kept us updated frequently. They actually have contact with the BNSF dispatch center! in Fort Worth? So they know where it is and when to load the shuttle depending on load. We were there during the summer and the train stopped everyday and always had to make a double stop. 
