Beijing Hutongs are these alleys in the Chinese capital city located mostly in the second ring road, that are what is left from the antique Beijing. Renting an apartment there can be great but be warned, the dream can be a kind of nightmare i you are not careful about a few things.
There is actually, to be oversimplistic but clear, two kinds of Hutongs. The renovated ones and the non renovated ones. The renovated Hutongs are simply fantastic to live in, but tey are now dramatically expensive. A few years ago, Chinese people tried to flee those areas that are associated with poor people in bad housing in China, but this is changing. The renovated Hutongs are now more and more expensive, rents have reached records heights and this is now very difficult to find an affordable one. If you have such financial means, take the opportunity, you won't regret it. Amazing places are for rent now.
If you can't rent a renovated Hutong, have a look on the non renovated ones or the ones that have been renovated but are still affordable, they do exist. You can find your dream Hutong by looking around, but this is not necessarily easy and you have to be a little bit careful.
You have to see generally the standard of the Hutong you are about to rent, is it a general good state or not, and have a look at very basic things such as the way the door closesn if it closes. This is true for the door of your apartement but check as well the door of the whole courtayrd that gives access to your apartment, to avoid bad surprises such as burglars.
Of course, have a look on the bathroom and if there is a bathroom, since many hutongs have common bathrooms are outside of the apartment, in a kind of spartiat comfort. Check if there is enough water pressure, if the water is hot and the state of the kitchen.
It is more convenient to rent a place which is not too far away inside the hutongs since this is going to be difficult to get there. It can be difficult to have your taxi to get you there and parking a car will be impossible, you ll have to rely on your feet and maybe the subway (but there is few subway stations inside the hutongs).
The intimacy can be a problem in the Hutongs since the accomodation are kind of imbricated. Check quickly the neighbours and make sure they are not some kind of lunatics.
See as well that the hutong you are going to live in has passed treatment against bugs.
Now, with these simple ideas go and look for your Hutong, the best type of apartment you can find in Beijing.