Kaiseraugst is a great place to visit. Over a large area there are remains of an amphitheatre, a forum and many other buildings stretched over fields in an area the size of a (Roman) city. In contrast to Rome and other big sites, this is just something you can wander around unrestricted, and trip over rocks in the grass which are part of building foundations.
It also has a good museum.
There is an annual re-enactment day (Römerfest), which is a lot of fun (real gladiator fights in the colosseum). This takes place last weekend in August.
Website here: https://www.augustaraurica.ch/en/
As for transport, don't panic. The Swiss transport system is "turn up and go", no need to look up anything 6 months in advance. Kaiseraugst is a commuter town outside Basel
Two ways to get from Basel to Augusta Raurica, either a local train to Kaiseraugst station, runs every 30 minutes, takes 12 minutes; then a 20 minute walk, past the Roman Tavern on the main road (I joke not).
Or bus number 81 from Basel, plus a similar walk.
See the "getting here" section on above website: https://www.augustaraurica.ch/en/visit/useful-information/getting-here/
Just buy a ticket from the ticket machine on the day.
You say "My husband will be traveling to Kaiseraugst,", will that mean you will be staying in Kaiseraugst, or in Basel?
"I am looking for day trips. I love nature, local cuisine, and meeting people!" - Basel is a nice town just for wandering around and taking in cityscapes.
There are day trips aplenty. Start with a day trip to Luzern.
Note on naming: The Roman town was called "Augusta Raurica", named after emperor (Caesar) Augustus. The modern town is called "Kaiseraugst" which is German for "Caesar Augustus".