The thing about prices in the Philippines is there seems to be no real guidelines as to what should be charged. You will find people overcharging online yet the same apartment can be a lot cheaper locally. The other issue there are people looking online for an apartment say its being advertised on somewhere like Cebu Classifieds for P6,000 they will then advertise it themselves for P7,000 or more in the hope that they can snag a renter and then skim off the top by making an agreement with the original advertiser. This doesn’t always work and in some cases they will be wasting your time completely because they never contacted the original advertiser and its already rented out.
So what would I pay in the City? I think you have to look at where it is in relation to everywhere else. For example there are a lot of nice locations near Ayala and SM Malls but also because they are near the IT park puts up the demand for workers sharing a condo or apartment. But I would expect to pay around P10,000 but I know other people renting some apartments in the same buildings for around P30,000 the biggest thing is taking some time out and looking around. There are agents that deal with the rental market but as soon as you introduce an agent your introducing extra fees. I would advise looking in local newspapers, asking on forums and searching the rental ads on things like Cebu Classifieds, Istorya and Sulit.
Remember also that as a foreigner they may try to hike the price so buying a sim for a cheap cell phone is also worth doing and doing everything via text messaging. That way you haven’t given your name away (second name is an obvious give away) and also people are used to dealing with people writing in English as well as Cebuano so nobody really picks up on it too much.
What are the usual terms for rentals? Normally its one months deposit and two months advance. But it varies property to property as sometimes they will let you move in with a month advance but generally the 3 payments is the standard method and amount expected.