I don't have any specific suggestions as I don't do a lot of cross country any more. But it would also help to choose a place that has lots of lakes so that the crowds are spread out. The Wallowas (a lot more than a few hours away) or the Alpine Lakes Wilderness are areas with lots of lakes. Some cross country lakes are nonetheless easy to get to.
A couple things to add. There are some trail-accessible lakes that are less popular. One example would be Wood Lake in Indian Heaven. And the only camping area is at the far end of the lake from where the trail arrives, so there would be some warning. Also, while Lookingglass Lake on Mt Adams used to be extremely popular, now that the trees around it are 100% burned very few people go there any more.