Look at the area on Google Maps.
See the airport north of town? A few miles south of it is Honokohau harbor - most of the dive boats are kept there. Zoom in and you can see there's nothing nearby. Many of the dive operators have their shops in town. Several are in an industrial park - Jack's Diving Locker is on Alii Drive just south of town. There's a few, mostly older condo complexes in town. If it's of interest, the King Kamehameha resort right downtown is a Courtyard by Marriott property.
Follow Alii drive south of town - it runs right along the waterfront. There must be 50 condo complexes mixed in with hotels and private houses all on Alii for about five miles to Keahou. The closest ones are walking distance to town on Alii Dr. Just south of town it's all lava to the waterline so the nearest beach is about 2 miles south.
A quick way to find the condo names is use Google Maps - type in condos Kailua-Kona and if you zoom to the 1000' level you'll see quite a few of them - it's all the small red dots - not just the ones with names. We were able to find a lot of options in the $100/nt range for 2 bedrooms. Some older, most oceanview or waterfront but not beachfront.
4 miles south of Kona is an area we stayed in. It's called Magic Sands Beach. White Sands Village is a large 2-3br. condo complex across the street. The back buildings don't have much of a view so they're cheaper. I've seen 2BR's in there for $89-99 nt. Across the street waterfront is Kona Magic Sands. It looks to be 30-40 years old and is mostly studios or one bedrooms but they all have windows facing the ocean. They're even cheaper. There is no food in that area at all though - the closest is probably one of the resorts a mile or so north. There's also a resort tax but some properties waive it.
At the south end of MSBeach parking lot is Mile Marker #4 - a shore dive site. There's one more nearby but I don't recall exactly where. The Kailua/Kona pier in town is one also. #'s 8,9,10 here:
http://shorediving.com/Earth/Hawaii/TBI/index.htm
We once found a really nice condo just a mile from Kona. No beach but it had a private pool. Recently renovated and $700 for the week. I don't recall the name but I found it - and all the others - on vrbo.com. If you don't mind a climb, look for upstairs units - many of the 2-4 level complexes don't have elevators so they're slightly cheaper. Some like White Sands Village are across the street from the beach also. I also found a few properties on the golf course near Keahou that seemed reasonable - no water view.
After Keahou it gets pretty remote all the way down to Captain Cook. And there's nothing north of the airport for 15-20 miles till you get to Kohala/Waikoloa.
hth, Alii Drive is on Google Earth so if you use street view you can see what's nearby. I used it to read the name of a condo complex.