could you reccomend a place of lodging near or in downtown close to the main sites for around $100 per night.
Eric, check the Cab Inn, a few locations in Copenhagen, small rooms, but just under $100 USD.
Besides Cabinn, also check a new budget hotel downtown ca 8. Mins to the Central Railway Station and Tivoli Gardens: www.wakeupcopenhagen.com - is simple and clean.
When are you going? Hotels are supposed to be cheaper in July/August when they don't have the normal business conference traffic. We stayed at Strand/Phoenix (reservation at Strand but they sent us to Phoenix when we arrived) and Opera (both near Nyhaven at the north end of Stroget) for $125 for a double. The price included breakfast, which was about $10 each, so the room was pretty close to your price. Euro was $1.28 then, about $1.33 today. If you're traveling outside of summer, you're probably better off with a bed & breakfast/pension.