there are ways you can make Iceland cheaper. Camping some of the nights is one thing to consider during the summer if you don't find hotel bedding to be important. There are pretty good camping areas in most towns all around the country.
You could also try www.couchsurfing.com, I know there are quite a few Icelanders listed there, at least in Reykjavik. If you plan on staying part of the time in Reykjavik I would try to be there over the weekend, for the nightlife, and spend the weekdays in the countryside. I think you don't really need to spend more than 2 days in Reykjavik in order to see and do most of the things.
And you can go to the Bonus superstores to shop for food and make your own lunch-box for the day, rather than living off hot-dogs from the gas stations
If you want to go whale watching I would recommend going in the North, at Husavik for example, or from Stykkisholmur, rather than from Reykjavik, as I think they have cooler sights over there (humpbacks are more commonly seen in the North and sperm whales and killer whales from Stykkishólmur.)
Personally I would also recommend that you'd come just a little bit earlier. In the beginning of August, the summer nights are already starting to get darker, but if you come in the second or third week of July you will experience the long summer nights, which really are the greatest aspect of the Icelandic summer.
On the other hand, like mentioned above, the first weekend in August is the biggest weekend of the summer for local tourism. That's when Icelanders have a long weekend and set to travel and there are lots of festivals around the country. That might be a hassle for you as there's more traffic, but if it's something that interests you it might also be a fun experience. The biggest festival is in the Westman Islands, a community of 4.000 people, but thousands of people gather there for this one weekend a year to party. If that's your cup of tea it might be interesting, but you can only get there by either boat or flight.
Lastly, if you plan on staying 3 weeks, I would definitely recommend going off the ringroad for a while and go inland. The highlands are spectacular (in my opinion) and not to be missed.
Have a great trip and don't forget to bring your swimsuit!