Shinjuku station is massive and crowded and can be somewhat overwhelming. But I still think it's better than Ikebukuro Station in terms of getting around by wheelchair and as far as flow of people being less chaotic. Shinjuku is certainly not the most expensive hotel district in Tokyo, but more expensive than places like Shinagawa and Ueno.

What's your hotel budget?
I'd encourage you to consider what's been advised: find a place with easy station access; get a decent hotel with enough space; be willing to take taxi at times.
Getting a hotel with spacious (>25m2) room within a few minutes' walk of a convenient train station would be ideal. For that, though, you may need to spend more than you'd like. But if you can afford it, I think it'll make the trip a whole lot better for your folks.