If you want to account for actual pay vs. advertised, you could probably model it to some order of effectiveness by applying a decay function of price vs. age of listing. This operates on the assumption that bargain rentals are on the market briefly, while overpriced rentals languish on the market.

I would get the data from the same authority that is tracking inflation - rent is included in the basket. In the USA I think the Bureau of Labor Statistics does the 'official' data collection.

Rent prices are pretty uniform - there isn't that much differentiation between properties of the same class (# of bedrooms and location, are what mostly matters; tenants don't make choices based on the type of furniture); so prices are relatively uniform - you don't have to ask a lot of people get those prices.

This is of course confirmed each time someone tries to create yet another index - if you use the same basket and weights, only rarely there are any differences in recorded prices.

Completely anecdotal, but their rental prices for Redwood City are in line with what I pay. The median prices they list for other cities seem to be in line with what I'm seeing looking at different places to live as well.