The best replacement for gazebo is pergola.

The best alternatives to gazebo are rated as following:
★★★★★  pergola
★★  umbrella
★★  canopy
★  screen house
★  cabana
★  tent
★  v-rep
★  webots
★  ramada
★  rviz
★  pagoda
★  pavilion
★  rotunda
★  marquee
  canopies
  tarp
  bandstand
  belvedere
  awning

Your alternative for gazebo is not listed? Suggest!
Speaking about gazebo, one probably shouldn't forget about hot tub.

Other search terms related to gazebo and their ratings are:
★★★★★ hot tub
You have in mind a companion for gazebo and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of gazebo in all years. Click on graph for more.
gazebo
pergola
umbrella