Visiting Assisi

There are direct trains Rome to Assisi.
Avoid Oct 4, Feast of St. Francis as it will be very crowded. Beautiful small city , well kept up by the Vatican. Views across the valley to Spello.

I see a direct bus to Assisi (3 hours) on Rome2Rio, but no direct train.

The train station is in the valley and you will need to take a taxi up to where the main tourist attractions are. Once on the main square near the church of St Clara it is a downhill walk to the Basilica of St Francis. The town is on a hill so walking from the valley and back down would be a real chore. Enjoy both of these two attractions, will take your breath away. Gorgeous religious paintings and town is full of history not to mention monks.

There is a regular bus from the train station to the town. You buy the ticket at the tabac/cafe in the train station which also has bag storage

I hope you are able to make it to Assisi as it is one of our most favorite places in Italy. You can find train info on the Trenitalia website. I plugged in a random date in May and came up with two direct trains to Assisi-one at 8:05 and the other at 2 something. Most trains going to Assisi require a change at Foligno. Also, you can check out the assisionline website for other info. If you scroll down, on the left you will see the heading "General Information" and under that "local opening times".

For getting to and from the rail station to Assisi, you may also find this helpful - https://www.italiarail.com/train-station/assisi-train-station-guide . Whether to choose taxi or bus will depend on your budget.

As a previous reply mentioned, there's a direct Regionale Veloce departing Roma Termini at 08:02, arriving at Assisi at 10:09 (time 2H:07M, current fares listed €11.70 PP). If you're buying P-P tickets locally, don't forget to validate before boarding the train on the day of travel. For the return, there's a direct Regionale Veloce train departing Assisi at 18:38, arriving Roma Termini at 20:50 (time 2H:12M, same fare). Be sure to leave lots of time to get back to the station for the trip back to Rome. Be sure to verify these times on the Trenitalia website before your trip.

To determine what sights will be open on Monday, I'd suggest having a look at the RS Italy guidebook, as the information is listed there as I recall.

With only one day in Assisi, I strongly recommend that you get a taxi from the train station and have it take you to the TOP of town, and drop you off at Piazza Matteotti, which is a main parking/transportation piazza; the buses mentioned in a previous post may well go there. From Piazza Matteotti, you will walk DOWN (and trust, me, it really is down) through town all the way to the Basilica. You will pass the main churches and sights (and restaurants) as you walk down the main street, the Via S. Francisco. You will end up at the Basilica. Give yourself a couple of hours to really drink it in! From the Basilica exit, keep to the street on the right as it curves around and you arrive at the big transportation piazza, Piazza Unita' d'Italia. (Study a google map, or Rick's map in his Italy book before you go.) You should almost certainly be able to get a taxi there. If you get to that Piazza and don't see the taxi stand, ask at the little gift shop/tobacco stand on the right when you enter the Piazza. They sell tickets to the various bus lines and could no doubt direct you to a taxi stand, or show you which bus will take you to the train station. The station is a couple of kilometers at least from the part of the city where you will be, and you don't have time to walk it.
Edit: and one more thing. A couple of times when I've been in Assisi, I've discovered that the taxi drivers are often called to pick up passengers by phone, and that can be the most efficient way to get one. If you get a taxi from the airport and like the driver, ask them for their card and indicate (talking, google translating, or writing it down) approximately where you will want a pickup from later in the day, and approx. what time. Let them know that you will call them when you are ready for a pickup, and confirm that they will be available. This may be the most reliable way of making sure that you get a taxi from Piazza Unita' d'Italia (or anywhere) when you are ready to go back to the train station. Also: don't dally when you arrive and exit the train station. I've experienced that there may be only a couple of taxis waiting - the drivers know when the trains arrive - and once they are gone, they are gone. (All of this advice is contingent of course, on the idea that you might prefer a taxi to the bus. I've taken taxis in Assisi when time is tight.)