Paige Pond Country Inn is a pretty guesthouse located pretty much smack dab in the center of the island. Rates start at about 55 US per night, and can be booked from their website.
The pros about Paige Pond is that they seemingly having excellent high quality accommodation for a seriously low price. Both the outside appearance and the rooms themselves are clean and well maintained, something that is not often done with accommodation this cheap, and all the rooms are fitted with AC, which is a godsend for some of the stifling hot days The furnishings in the rooms are relatively new, none of that "rustic" (aka run down) look that you get with other cheaper places, and you have a decent kitchenette in even the cheapest rooms, as well as FREE wifi. It's far away from the hustle and bustle of St. John's/English Harbour, and the views just a little way down the road are simply spectacular, as they look over the valley of the Body Ponds.
On the other side, the cons are that this place is pretty out of the way. It's in the middle of the island, far away from the main points of St. John's on the northwest, Jolly Harbour on the southwest, and English Harbour in the south of the island. There aren't any supermarkets in the area, though there is a small onsite shop that will provide the bare essentials. There is a bus service on the route, but if you're intending on enjoying the nightlife you may be better off renting a car, or taking a taxi, especially at night.
The verdict is, Paige Pond is a great budget buy, clean, cheap, and comfortable, and lots of useful amentities. Well worth it if you're willing to rent a car or are willing to take the bus, though you will have to stock up on supplies if you'll be staying here for a while.