I focus mainly on the landscaping when I visit dream towns. I can't say I do it for "inspiration" like others, more like appreciation. Because seeing something in a dream town isn't likely going to affect how I design my town, you know? But I still like to see what others do with their towns
Something I should do more is look through the house interiors. I admit I often skip this when visiting dream towns, just because there are often so many rooms, and looking through them all could turn into a long visit.
My dream visits are often pretty short. Thinking about this, I find it a little funny that I meticulously think about every inch of my town, and every room in all my characters' houses, when it's likely that visitors to my dream town are the same as me, just breezing through everything and skipping many parts
Though I'll say that I often spend more time in towns of WiFi friends who I haven't WiFied with in a while for whatever reason. I guess it's because I miss WiFing with them, so visiting their dream town is the next best thing. And I'm more invested in their town (rather than a stranger's) since I know them, so I find it more interesting to explore and see what's going on.
I never focus on the villagers much, except for taking pictures of their houses for my villager house exterior collection!