Is there a way to get new surroundings in Miitomo?

No, there is no way to purchase furniture, wallpaper, or other items.

With the release of version 2.0.1, it is now possible to edit wallpaper, flooring, and posters.

To edit your room, tap on the menu, and then hit "Customize Room".

The menu is similar to the clothing with different tabs for the types of items, but it could be easy to miss the "hide furniture" button that is above the menu.

Note that spaces for posters cost money (real life money), but the first space is free. These posters can be one of your miifotos or an image from your device.

As for getting new wallpapers and flooring, there may be events that give out special types, but there are also Drop boards that have them as prizes. Furniture appears to still be something that cannot be bought/won.