I want to install Steam on two different locations

I would like if possible to install Steam at two different locations, physically separate on two different IP addresses (MACs) and can play games purchased. It's my house and my cottage, where I could play on both computers.

Short answer: yes, it can be done

As Steam is a cloud service, this is percisely what the platform excells at.

If you have two differents computers, simply install Steam, log into your account, download the games you want and play on. If you have Steam Guard enabled, Steam may ask you to verify the new location by a code sent to you by e-mail.

However, some games may have additional DRM that limits the number of computers the game can be installed on during its lifetime. But these are not tied to Steam or your user account.

Edit: I've been told in the comments that you can now log into same account on multiple computers to use something called In-Home Streaming. You just can't play games on both of them at once. Altough, this seems to be limited to same home network. Anyways, thanks Kexlox.

Also, here are links for more information on Steam Family Sharing and Steam In-Home Streaming