I don't have a basement but I did ask Sonic to install the ONT into my server closet and they were happy to do that. I much prefer that so that all my networking equipment is hidden in a closet (I'm using ceiling-mounted wifi access points, so wifi connectivity isn't an issue). The fiber runs from the street to near my roof, down the side of the house, along the side of the house to an opening, into the crawlspace under the house, then up into the closet.
Note that the installers do NOT wall fish - they'll only either go directly through an exterior wall to the outside, or through the floor (if you have a crawlspace or attic under the area you want it installed). They may be able to run the fiber through a wall if you drill a hole yourself and provide your own pull line through it that they can tie the fiber line to and pull it up with.
I ran Cat6 cable to most rooms though. If your house is not wired for Ethernet, you might just want the Sonic ONT to be installed in a living room or something similar.