Travelling alone - need help on the itinerary

Welcome to the forum ashbaby. The 5 day Swiss Flexi Pass sounds like a good choice indeed. If you need public transportation in Basel on day 4-6, that will also be discounted by 50%. As for day 2 and 3 of your itinerary: you don't necessarily have to cover both the Schilthorn and the Jungfraujoch. They're both stunning in their own way, but I think visiting one of them will be fine too, especially if weather isn't that good. If you want to do both, you should combine the Schilthorn, Mürren and the Trümmelbach falls on one day, and the Jungfraujoch, Kleine Scheidegg, Wengen and Grindelwald on the other day. Spiez can well be combined with a boat ride over lake Thun. This can be an afternoon activity after a visit to Schilthorn or Jungfraujoch.

Have you considered staying in Lucerne instead of Basel on day 7/8? It will save you from traveling back and forth between Basel and Lucerne. Traveling times from Basel to Zurich and from Lucerne to Zurich are pretty much the same. In case you still need hotels: these lists for Bern, Basel, Lucerne and other towns may be of help.