Unfortunately, there are no Google Searches that render good suggestions for cheap sites that create beautiful flowcharts. The recommended products seem to either be locally installable or exorbitantly priced.

I now present two. They can both import from Visio, can both integrate with Confluence, and both cost between $5 and $10 a month.

Gliffy

• Slighty more “comical” and flowing, but the difference may be negligible
• Google Documents integration available with all paid accounts
• Has an academic discount

Lucidchart

• Less effort and less clicks to control alignment and establish links than most services
• You can leave comments on components
• Revision history
• Integrates with Google Documents, but only with team accounts
• You can do Hangouts and chat from the design screen.

Edit: I also received a last-minute mentioned for draw.io from @DiegoTerzano. Though the designs are thinner/leaner, it’s not a shoddy interface.