Most restaurants want wallpaper, but are unable/unwilling to articulate that desire. In general, musicians in restaurants are hired to provide the appearance of "class" and "culture" while providing music at a level designed only to prevent any awkward silences in conversation. Have a listen to the level that the piped-in music is playing at when there are no musicians--that's the preferred level.
When you're trying to get booked, emphasize your "venue-appropriate volume" early and often. If you get booked, make sure that any monitoring system you bring is completely independent of the audience-facing amplification so that you can hear yourself over the surprisingly loud audience conversations without interrupting them. No restaurant manager has ever gone over to the band during the evening and said "Hey! Can you guys turn it up a bit?!!"