Sunshine Village ski resort near Banff stays open every year through to the end of the May long weekend, so depending upon your exact arrival date, that might be an option for you if you want a day or two of downhill skiing or snowboarding.
The odds of temporary road closures due to bad or winter road conditions are very, very low in May... I hope I didn't give the wrong impression! The road closures I refered to, in the Canadian Rockies national parks, are roads that are closed seasonally. (Sightseeing traffic is low through the winter, so the parks service saves money on road clearing by closing them... also many of them have areas where avalanches would be a hazard.) They open for the summer at various times, ranging from the May long weekend (for the Miette Road here in Jasper NP) to later May/early June (Moraine Lake Road, Yoho Road) to mid-June (Cavell Road).
Note that in May, the high country is still snowbound, so hiking is confined to lower elevations. There are tons of great hikes that will be accessible, but these are not the flower-filled subalpine or alpine meadows you see in glossy photos.
If the location is convenient to you and what is offered there suits your needs, then LLJ is as good a overnight stop as anywhere else. I haven't stayed at the motel there but have camped at the nearby provincial park. It's quiet, and as mentioned by mufti, out in the middle of nowhere. Other options? Personally, I don't care much for Kamloops but there are lots of hotel and dining options there, so it is a logical choice. I really like the small town of Revelstoke, but that's six hours from Jasper, backtracking via the Icefields Parkway. The parkway is definitely worth driving twice, but the other route (#16 and then #5 towards Kamloops) is also scenic (just not quite so dramatically so). Clearwater is one option on that route, four hours from Jasper and one from Kamloops; it's the entry point to Wells Gray Provincial Park, if more mountains and waterfalls appeal to you.
If you are active (and not 60+), the one disadvantage to most coach tours is that they are heavily weighted at sightseeing only, with no time available for outdoor activities; if they do have a free afternoon built into the itinerary, you don't have transportation available to get to a trailhead etc. They also tend to be early starts and the one you included the link in your other thread was a lot of time on a bus, seeing scenery passing by.