The site is good but you can get the same type of service if you buy "El Comercio" on a Sunday.
If you want to stay in Lima for a couple of weeks it would be best to stay in a hotel because you'd probably spend more on food and other services that type of websites offer.
Hope it helps.
I disagree. Staying in a hotel is much more expensive then renting an apartment. My folks and another couple rented one last year for 9 days, and it was $500 total. A hotel would've ran them at least $60 a night per couple, so about $480 a week as opposed to $250 for the week. The apartment also had maid service for available for daily or weekly cleanings for a minimal cost. They were also able to do their laundry in their apartment, something that couldn't be done in a hotel.
Also, we used this site, which may be a bit more expensive than other options, but I am not positive on that:http://www.mirafloresapartmentrentals.com/