If you're looking at SE Idaho specifically, I'm assuming you're looking primarily for outdoor activities. There's obviously some good hiking and areas over the border in Wyoming (Periodic Spring) and up into Jackson. And south you've got the areas around Logan (Naomi Peak, Wind Caves) and down into SLC.
As for Idaho, Idaho Falls is a nice city, but not a place that would draw me for a weekend stay. It's more of a gateway to the national parks to the east.
Your best bet if you're looking for a city to explore is probably Twin Falls. There are a lot of activities along snake river. Hiking, viewpoints, parks. And downtown is nice to walk around in. Shoshone Falls, Perrine Memorial Bridge to watch some base jumpers and for the views, Perrine Coulie Waterfall, Canyon rim trail. Elevation 486 for some nice views and dinner. Koto Brewing for excellent beer and some really good (and unique) apps.
The downside of that is, other than a few waterfalls (Cauldron Linn) and viewpoints to the east, there's not much surrounding Twin Falls.
I will mention that The Cookie Place is a must stop if you make it to Pocatello or Idaho Falls. And if you are somehow in the area, Wick's Steakhouse is a cool spot for dinner in Declo.
More toward the center of the state, but Sun Valley/Ketchum and then up through the Stanley area is a gorgeous spot to spend some time.
