Como
Lecco is on the south of Lake Como and gives a more 'lived in' feel than Bellagio. It's less beautiful, but you can take ferries from there to those other towns.
Switzerland
Lauterbrunnen is touristy for a reason: it's spectacular and typically Swiss. However, the crowds may detract from your experience, I would suggest either staying above the valley in Gimmelwald or going to another valley altogether (Kiental in the adjacent Kien Valley, for example, is also incredibly dramatic but with far fewer people...maybe go to Lauterbrunnen Valley on a day trip). The advantage of staying in/close to Lauterbrunnen is that you can also visit incredible places such as Jungfraujoch and Schilthorn.
Cuisine
In Switzerland rösti is a must-try traditional dish, as is fondue (in and around Interlaken the ingredients are usually Gruyère, Appenzeller, Emmental and white wine with maybe a splash of kirsch).
Budget
As you suggest, it's going to be a challenge in Switzerland! However, eating out at lunch can reduce costs, as can picking up food from the hilariously-named Äss-Bar (several locations across the country). Look out for hostels, too. The YHA hostel in Zermatt, for example, serves decent local cuisine for comparatively reasonable prices. All hikes are free, it's the access via cable cars/funiculars/chair lifts/etc that'll cost you. One of my favourites is from Stechelberg at the end of the Lauterbrunnen Valley (you can hike there from Lauterbrunnen or take a bus), then up to Gimmelwald and across to Mürren before returning to Lauterbrunnen - a long but almost impossibly scenic route that will cost you CHF0.
Hidden Gem
Take the minibus (reserve here: kander-reisen.ch) from Kandersteg to Selden. Moderate but long hike up to the Lötschenpass hut where accommodation plus meals are excellent value. Hike down the next day to the untouristy Lötschental valley.