I am developing a website for a client and I am trying to find out what I should be charging them for hosting the site. Is there a standard price these days?
The hosting costs should be payed directly by the client. In other words, it is the client responsibility to buy a hosting solution. You are just the web developer. Not the IT department of the client.
You role there may be suggest a hosting solution that will serve the needs of the website you have developed.
That way the client can change the hosting solution when they want. If it is you who pay in their behalf then it could be a mess.
I am assuming that you are not going to be the sysadmin. If you are going to be the sysadmin then you should of course make the client pay you for that too. But the client should be the one who pays the hosting costs in any case.
There isn't really any one standard price. You could pay as little as $2 per month for a shared hosting account, or several hundred a month for a big dedicated server.
The best thing you could do is find them a host and hold their hand through sign up. As long as you have the password, you can get in to make any changes you need to. And that takes you out of the payment loop.
If they don't want to deal with the host at all, then you'll have to sign up for the account and charge them whatever the cost is plus some profit for yourself... consider it a management fee. The problem with this method is the host will bill you monthly like clockwork, but this client may not always pay -you- on time, leaving you holding the bag for the charges.