February, Sofia is still extremely cheap. The Hilton can be had for <60€ per night. The location is not super central, but convenient next to the subway, but that still means a short walk (around 300m) to the station, taking the subway to the centre from there.

Considering in February the differences from "downtown 5*" hotels to the Hilton aren't that big, I'd probably stay in the centre (Serdika) itself.

Sofia Hotel Balkan is probably the "can't take it wrong" choice.

Arena di Serdica has the most unusual lobby and is also a fairly safe bet, especially if you're into history.

Also, if you like to tell me when exactly they're there, I can give them a personal tour