If you're coming with luggage, I'd recommend storing it before exploring. There are several coin lockers around Atami Station, as well as staffed luggage storage services. I left mine at ATAMIX before walking around the shopping streets. Otherwise, with the crowds and stopping to browse the shops, dragging luggage around would be really tiring.
The shopping streets in front of the station, Heiwa Street and the neighboring Nakamise Shopping Street, are packed with stores, but their biggest feature is the huge amount of food. In addition to Atami's signature onsen manju and dried fish, as well as Atami Pudding, which has practically become synonymous with the city, there are also dessert shops that have become popular in recent years. Still, Atami Pudding remains the most popular dessert.
I originally wanted to try Atami Pudding too, but gave up as soon as I saw the line. I had more plans afterward and didn't want to spend too much time waiting. As I walked around, I noticed that it wasn't just the pudding—many famous shops can have long lines during peak hours, so I canceled my plan to eat here.
Overall, Atami Heiwa Street Shopping District has the lively atmosphere of a hot spring tourist destination, with long-established shops, souvenirs, and modern desserts all mixed together. It's quite a good place to buy souvenirs, so I'd recommend stopping here for some final shopping before leaving Atami.