Lima has quite a bit to see - certainly 3-4days but to fill a week... probably not - you are better spending a few days in Arequipa (Colca Canyon) or heading north to see a bit of the country there. I seem to remember reading in the guidebooks there were some interesting ruins north of Lima that you may be able to see on a day trip, or on an overnight trip.

As an FYI you can easily (and pretty cheaply) fly between the various Peruvian cities if you book ahead with LAN for perhaps $70USD pp per leg on one-way fares rather than any buses between places. Personally I did Lima-Arequipa-Cuzco-Porto Maldonado-Lima and don't remember it costing too much (was short of time). You may find it saves money (and is convenient) if you book your own airfares and meet a guide in Cuzco.

Also worth mentioning that the Marriott is a lovely hotel, it would be nice to spend quite a bit of time there, but there isn't a nearby beach (it is about 300m away, but down a huge steep cliff so you need to take a detour) if you wanted a relaxing bit of beach time it wouldn't work so well - and other than having food/nightlife nearby there isn't going to be much to do during the day.

Enjoy your trip!