Vienna is a great city to explore beyond the usual. For less touristy experiences, definitely check out the Spittelberg quarter, especially if you're there in late October; they have a Christmas market starting mid-November, but the area itself is charming with small galleries and shops year-round. It feels very local.
For food, it’s a bit tricky with celiac, but there are some solid options. Zum Wohl (Stumpergasse 61) is a 100% gluten-free restaurant, so you don't have to worry about cross-contamination at all. It's a bit pricier, expect around €25-35 for a main course, but it's completely safe. Another good one is Gasthaus Posch (Meidlinger Hauptstraße 72), which has a dedicated gluten-free menu and good understanding of celiac needs. Always double-check when ordering, even if they say they're GF friendly.
For a unique market experience, the Brunnenmarkt in Ottakring is much less touristy than Naschmarkt. It's lively, multicultural, and you'll find everything from fresh produce to spices. It's more of a local market feel. For a day trip, consider Baden bei Wien. It's a short train ride (around 30 minutes) and known for its thermal baths and a lovely casino. The town itself is quaint and walkable, and you can easily spend half a day there.
Also, don't miss the Hundertwasserhaus, an apartment building with a unique, colorful design. It's residential, so you can't go inside, but it's a very different architectural experience than the imperial palaces. It’s a nice walk through a less touristy part of town.