Someone already mentioned Microsoft Essentials as a good fit for what you are asking. And I have to second that. It's a good solution to have as your real-time protection.
If you want another scanner for a second opinion, mainly when you install new programs, or transfer new documents (emails, usb key, etc...). You're better off using something like
VirusTotal or
Jotti.
Both allow to upload files for them to be scanned. It is similar to the cloud feature you don't like, but it's manual so you can choose which files you want to send, not automatically dumbed down like cloud AVs. Moreover both services use a pool of AVs (50+ for VirusTotal, 22 for Jotti) with the latest virus signatures definitions. It is much safer than having only 1 or 2 local scanners.
VirusTotal also allows you to scan based on the hash of a file. This allows you to bypass the 64MB upload limit and is also better for privacy. If the hash is already in its database it will show you the latest scan on the original file.
Apart from that, there are other solutions that work well as on-demand scanners, to be used locally as an aide for your main AV. If they connect to Internet, it's only for signatures updates, some don't even have that feature and you'll need to reinstall the app (or its virus definitions) regularly by yourself. Most of them can also be found as portable apps (
Portable Antivirus Firewall | Category) which don't need any install and can be run from usb/external drive :
ClamWin
Microsoft Safety Scanner
Kaspersky Virus Removal Tool
Dr. WEB CureIt!
McAfee Stinger
Emsisoft Emergency Kit Scanner
Some are advertised as removal tools, but they are actually regular scanners (old school like you said) based on the same engine and virus signatures as the full security suites. They just don't include all the fancy features (real-time protection, cloud, etc...).
N.B: I tend to also agree with what Alejandro85 said. The "cloud" is mostly marketing hype.