Mount Lavina Homestay is a comfortable guest house in Colombo, about 5-10 mins walk from the city. It is one of the best and cheapest accommodations available here, and very well-liked by tourists. 

Here is a review,

I had a pleasant stay. The property is just a short 5-10 minute walk from the busy main Galle road. The owner is kind, honest, friendly, helpful and speaks good English. There is internet and satellite tv in the living room. Also we are free to use the kitchen.

(Source: Mount Lavinia Reviews)

Address: 17/7 Off De Saram Road, Mount Lavinia, Colombo, Sri Lanka 10370

Tel: +94-112-735205

Rate: $7 per night; Click here for online booking.

Situated at Dehiwala, Adikaram Hostel has a beautiful sea view, and hence the name. This is another famous tourist rest spot, away from all the city bustle. Although the hostel is quite popular, the rates are very cheap, the rooms are well-maintained and the service is excellent.

Here is a review,

This is the best hostel I've ever been. The dorm beds are new, the sheets are clean and my mattress was very comfortable. The whole apartment is kept very clean and tidy. You get a great view from the balcony and also from the roof top to the ocean. You have a nice sandy beach in front of the door. A standard breakfast is being provided. Internet and Wifi is available free of charge.

(Source: Reviews)

Address: 45/1 , Initium Road , Dehiwala , Colombo, Floor 3 , Apartment 2, Colombo, Sri Lanka

Tel: -

Rates: $8 per night; Click here to book online.

Chamenka Guest House is a clean, comfortable and very pleasant guest house at a walking distance from Dehiwala Junction. The owner of this guest house is exceptionally praised by every guest, and is considered helpful and very friendly. A very good accommodation, at a cheap price.

Here is a review,

The owner was friendly and very helpful in organizing our futher journey. He gave useful advice about Colombo and travelling in Sri Lanka. He offers trips to other destinations in Sri Lanka.

(Source: Travellerspoint)

Address: No 44, Pallidora Road, Dehiwala, Sri Lanka

Tel: +94-11-2715102

Rate: $10 per night; Click here to book online.

Located at a 15 min distance from the main city, Hornbill Holiday Home is a very good place to stay. Although it is a bit higher than your given budget, the hotel is very well maintained, the rooms are spacious and the service offered is nice.

Here is a review,

Hornbill is the cleanest hostel in Colombo. It's down a quiet lane, a short walk from the train station and a beach, in a secure compound. The staff is very fast, and don't slack on duty. The owners are nice people. Hornbill is good for those who seek a quiet life!

(Source: TripAdvisor)

Address: No 21A, Fernando Gardens, Dehiwala, Colombo

Rate: $15 per night; Click here for online booking.