Bern in half day

What's worth doing for you depends on what you're interested in, of course, but I thought Bern was a very attractive small city, and I'm glad I stopped there. Your plan for 2-3 hours will give you plenty of time to do the "Heart of Bern" walk in the Rick Steves Switzerland guidebook and/or to wander around a little bit on your own.

Yes, Bern is worth ½ day. Nice old town on a bend in the river. Don't forget to say hello to the bears.

As with any city in Switzerland (and most of Europe), make sure you have a plan where to park before starting your journey. The city centre is car-free and is surrounded by car parks (pay).
Official website listing all the offstreet parking is here: http://www.parking-bern.ch/e/

A similar problem applies in Interlaken. Have you checked that your hotel has parking? Even if it does, you may have to pay.

Thank you for suggestions. I was thinking about Rick Steve's guidebook, that is why I consider 2-3 hours walk.
Rick suggests to park at the train station.
In Interlaken we stay at Hostel Backpackers Sonnenhof, where they offer free parking.

Any suggestion for a nice not too expensive lunch place in Bern?

The website I listed earlier ( http://www.parking-bern.ch/e/ ) includes the "Bahnhof Parking", P1 on the map. Prices:

Basic fees and first 30 min. CHF 2.20
per additional 10 min. CHF 0.70

So 3 hours will cost you: CHF 2.20 + 2.5 x 6 x 0.70 = CHF 12.70, about what you would spend for a coffee and a cake per person. Full lunch (one course) will be CHF 15-25 per person.

If you go all the way to the far end of Bern city centre (farthest from the station), across the bridge, the bear pit is on your right. The adjacent building (tourist info office) includes a restaurant, the "Altes Tramdepot". Menu here: https://www.altestramdepot.ch/uploads/files/pdfs/Speisekarten/2018/Sommer%202018/Summer_2018.pdf
If you want to keep the costs down, larger branches of department store Manor, or supermarket chains Coop or Migros have restaurants. All three have branches in central Bern.

"Not too expensive" by Swiss standards or American ones?

Whatever your budget, if the weather's nice I recommend having a picnic. All over Bern there are places with plenty of benches and great views that are wonderful for just sitting for a while. Two that come to mind are the City Park (Kleine Schanze, just south of the train station) and the Münsterplattform (adjacent to the cathedral, and on the route of the walking tour).

For provisions for your picnic, there are bakeries all over town where you can get a sandwich and a cookie, or similar, for around CHF 7–10. There's also a place called "Äss-Bar" (at 19 Marktgasse in the cellar) that buys up all the leftovers from other bakeries and sells them the next day for cheaper prices.

There's a Thai take-away stall at the corner of Schauplatzgasse and Christoffelgasse, just inside the Loeb Lebensmittel store. The food is not terribly exciting (similar in selection and quality to what you'd find at a fast food Chinese or Thai counter at a mall food court in the US), but it's filling and you get a generous portion for around CHF 10.

The vegetarian buffet chain Tibits (with two locations in Bern, one in the train station and one in Gurtengasse) has some really tasty food, in my opinion. You pay by weight, and the price is a bit less to take away than to eat in the restaurant. A moderate-sized takeaway lunch is around CHF 15–20. Note that you get one free piece of bread per plate of food. (There are signs that tell you this, but if your German's not so good, you might not notice them.)

Thanks
You are right ... American or Swiss standard. I forgot about this
But i like every suggestion , helps me to move around easier.
I cannot find Rick’s Bern tour ..hm

We were in Bern for about 3/4 of a day. We felt it was a very interesting and enjoyable day. Make sure to see the clock tower and look for the fountains--especially the "baby eater". We went to the Einstein exhibit within the history museum. It is extensive and well done. There is a huge Coop store close to the train station. We often purchased picnic supplies at the Coops around Switzerland. They are well priced with bakery goods, chocolate, wine, etc.

The "tour" is the walking tour outlined in Rick's book.