Can I create a dashboard that let's the user pick which groups of servers they want to see?

You should be able to achieve this with UIv4 and dashboard filters. It could be as simple as using system.groups as your filter:

Or you could get more creative and apply additional properties to your devices, either individually or at group level e.g.

• role: webserver/appserver/etc.
• location: US/CA/etc.

You can then filter using one or more of these properties.

Within the dashboard itself, you can also define which properties should be populated by default.