>> Is Grindelwald busy /crowded in late May?
I wouldn't think so. The ski season will be over, and the hiking season will not have started. For that reason, many accommodation establishments close until there are more people about. The hotel I stay at in Wengen closes for the month of May, as well as October, November and most of December. That is a fairly common pattern, but there will always be some places open.
>> Wondering if it is worth staying there instead.
It's certainly an option, especially if you can find cheaper chalets there. Bear in mind that the less expensive options are likely to be further away from transport. Grindelwald is very spread-out and hilly. There is a town bus service that runs until shortly after 7pm. It would be useful to be aware of where the bus stops are before you choose accommodation that is a long way from the station. Google Maps has the bus stops marked.
>> I've heard it might be too touristy though
Well, everyone has their own opinion about that! Grindelwald is in a splendid alpine setting, but there is car traffic in the village, and bus tours can also get there. There are more shops and restaurants than in Lauterbrunnen, Wengen or Mürren, so it has a busier feel. That suits some people. Others prefer the car-free villages. It's simply a personal preference.
>> My parents are travelling with us. While they wouldn't mind walking all day exploring the pretty mountainside, I'm thinking it might be easier to pick a place near the train stations, or at least not a lot of uphill walking involved to get home at night.
I've mentioned above that Grindelwald is hilly and spread-out. That also applies to Wengen. There are some pretty steep areas below the station, but you would be walking uphill in the morning and downhill at night.
People staying in hotels are usually picked up and dropped off with their luggage on the day of arrival and departure. I don't know what the arrangements are for people renting chalets.
The flattest part of Wengen is the Dorfstrasse, from the station to just before the Hotel Schönegg. That area has most of the shops, restaurants, and a number of hotels. The chalets tend to be scattered about the slopes.
Lauterbrunnen, while not entirely flat within the village area, is definitely flatter on the whole than Grindelwald and Wengen. And of course, there is a bus service through the village and on to Stechelberg. Those bus stops are also marked on Google Maps.