Hotel stay in Wengen, Switzerland

You can't get much closer to the train station in Wengen than the Hotel Silberhorn. It's just across the walkway from the station platform:

http://www.silberhorn.ch/en

There are rooms with views to the valley and also rooms with views to the backside. Make sure you specify a "valley view".

Tim got there first, the Silberhorn is excellent, across the street from the train station. There may be some slightly less expensive establishments nearby. Anything in Wengen should be pretty decent.

We have 2 adults and 2 kids. My budget is not more than $300/night.

I just looked at a weekend in June and a quad room is a bit more than your budget at the Silberhorn, but not excessively ($370/nt). It does include breakfast, and it is top of the line.
The Victoria Lauberhorn is just a block away and in your budget range ($300/nt).

I have also checked the rates of Victoria Lauberhorn and hotels.com is showing $249/night. Is it far from bus/train station? I am just thinking about my 2 kids.

Take a left walking out of Wengen station and the back door is like 50 meters away.

Most hotels are going to be easy as Wengen is pretty small. We were there last month and stayed at Hotel Baaren. They have the best restaurant in town and if you do the half board, it's an incredible value, especially given meal prices in Switzerland.

I stayed at the Hotel Falken last May with my husband and 2-year-old. They provided an infant cot for the 2y.o. I didn't investigate the family room options, but I believe they do have them. We liked it -- classic, small old Swiss hotel. The only downside was that you could hear folks in other rooms, but I'm sensitive to noise so your mileage may vary. We met friends there -- two other couples there who brought their dogs, and liked the views all around. We walked from the train station, but if you give them advance notice, they'll send the cart down to help you to the hotel. I believe several hotels offer this. It's a car-free town otherwise.
http://www.hotelfalken.com/en/

Wengen is very small so getting around will not be difficult. We stayed in a studio apartment that may be too small for your family, Le Voila, but they have a larger apartment next door. There is a mini golf course, playground and pool in Wengen.