Furnished housing is by far more expensive than unfurnished housing. So if you're planning on staying for a bit, go for the latter option. In Lima, your best bets are San Luis, Surquillo, San Miguel, Jesus Maria, Lince, Barranco, Chorillos and some parts of Surco and San Borja. We spent about five months in Miraflores, one of the top-end districts in Lima. I hated it. We constantly battled mold as it was near the ocean. Now we live in Surquillo, have a much bigger place and have no mold. You'll probably spend about 100 to 200 USD on housing. Another plus about living in the districts above is that utliities are cheaper. We pay half of what we did in Miraflores.
Although many foreigners and some Peruvians will tell you that the combis, buses, aren't that safe, I think they're a lot safer than taking taxis and heaps safer than driving yourself around. Combis have routes they follow, unlike taxis which weave all around. Combis charge you a set rate, but you have to ask a taxi driver how much it costs beforehand. If you look foreign or don't speak Spanish, expect to be charged double. I enjoy taking combis, you tend to run into people you know, a good place for people watching. Most combis charge one sol or 1.20 soles. A 45-minute combi ride to work is only one sol. If you're going for a short distance, you should only pay a china, 50 cents, but be sure to ask before you get on the combi.
There are lots of supermarkets, but prices tend to be higher than in other places. Eco is a cheaper supermarket. It carries the same things as more expensive supermarkets, a branch of the Wong supermarket. We go to Eco weekly and probably spend about 60 soles, whereas if we went to other supermarkets, we'd pay nearly 100 soles for the same things.
Another good place for grocery shopping is the market. Markets are all over the place. They allow you to get a glimpse of how Peruvians shop. You'll find fresh foods and veggies, even homemade sauces, such as aji.
Markets are the best places to shop. Be sure sure to ask for a discount; you can usually get a couple of soles knocked off. In general the shops in the front charge more than those inside. A tip, if you're going to a market, make sure you wear old clothes, no jewelery and hide your money well.
Polvos Rosados is usually where tourists go, but if you cross the streets to Polvos de Higuereta, you'll find better quality, cheaper prices and a cleaner atmosphere. Next to Polvos Rosados is CC de los Altos, which is right on Ovalo Higuereta in Miraflores. There are lots of little kiosks.
El Hueco in Abancay in the center and El Mercado Central are huge markets. I've gone to both, and prefer to go with my husband rather than alone as it's in a bit of a rough neighbourhood. If you look foreign, I wouldn't recommend it unless your Spanish is super. You can find good bargains, though.
People come from Chile and Ecuador just to go shopping. It's a sprawling market with blocks and blocks of shops.
A good place for furniture is Plaza Hogar in Av. Angamos in Surquillo. We just bought a dresser and closet there for about 200 USD. Things are often made by hand (even sanded by hand), and you can choose from different woods and varnishes. Av. Angamos also has lots of stores that sell matresses.
There are good freebie places in Lima, such as Parque Kennedy, the Plaza de Parmas, Parque de la Muralla, or the Cathedral of Lima (but only on Sundays during Mass). You can also walk along Larco and look at all the souveniers that shops there sell.
If you're going into discos, go a bit early, around 10:00; prices tend to be cheaper then. Movies usually have lower prices on Tuesdays. Many pizza joints have two-for-one deals on Tuesdays and Thursdays. For restaurants, look for the smaller hole-in-the-wall places off the main streets. Not only do they usally have cheaper prices, but the food is better. Beaches are also free and great places to relax and people watch.
By staying off the tourist track, planning and a bit of sacrifice, you can easily live off of 500 USD a month.