Assisi, Florence or Rome

Since you are allowing so little time for Florence, I am assuming that art and museums are not really important to you. Is that true? If so I would leave Assisi in your schedule since it will provide you a taste of something different from your other stops. If art is important to you, I would add time to Florence, possibly by skipping assisi and taking another day away from one of your other stops.

I would rearrange the nights a little, 4 nights Venezia, 3 nights Firenze, 2 nights Assisi, 6 nights Roma. Adds up to the 15 nights you have allotted.

Your allocation of nights is not what I would do, as your plan is really Rome-heavy. I don't know if this is you first time in Italy, but you could consider the following for your 15 nights on the ground and including only the locations you mentioned.
Venice 3 nights (with day trip to Murano and Burano islands)
Florence 5-6 nights (with multiple day trips in Tuscany, e.g. Siena, San Gimignano, Volterra, Pisa, Lucca, Arezzo, Chianti hills, Pistoia, and many more, including Bologna, in Emilia)
Assisi 2 nights
Rome 4-5 nights (with day trips to Orvieto, and to Pompeii or Ostia Antica)
You can adjust some nights up or down, but this plan will give you the opportunity to see more. Florence itself can be visited in 2-3 days, but it's very strategically located as a base for a lot of important tourist locations like the ones I mentioned in parentheses above. Also try to avoid one night stays, which are a time waste (all those checkin and out) and not relaxing. If you go to Assisi, spend two nights.

Most everyone here will tell you to rearrange the days, giving up a day or two in Rome. If there is a specific reason for 8 nights in Rome then that's what you want to do, otherwise I would do: Venice 3 nights, Florence 4 nights, Assisi 2 nights and Rome 6 nights. You're very wise to choose only 4 cities for your 15 nights, that lets you enjoy them a little slower and that is good. So many people would try to pack in so much more in 15 nights.

It takes a long time to get from Florence to Assisi and from Assisi to Rome, so I would spend 2 nights there, taking a night from Rome. Assisi is much different from your other stops, and I found it much different from anywhere else I've been in Italy, so I encourage you to visit there.

Mary, I agree with everyone else, Rome is great but it would be best to spend some of those nights getting to really experience your other stops, unless you have some special event causing you to spend that time in Rome. Also, while Venice, Florence and Rome are all wonderful, I myself think it would be a shame to spend two weeks in Italy, without experiencing the different nature of one or more small towns, whether Assisi and others in Umbria, or the hilltowns of Tuscany, and ideally spend one or better two nights in them rather than a day trip or times when day trippers are plentiful there.

One more vote for at least two nights in Assisi.

We stayed five nights in Assisi and hated to leave. Never ran out of things to do. We'd go back in a heartbeat. Best times in Assisi are in the evening and early morning, when the daytrippers are gone.

Photos here.

Thank you everyone for all the great replies!
I am going to review our plan and make some changes. For sure we will now do 2 nights in Assisi.
I love art, but my husband is only good for so much.....so I am trying to make things interesting for both of us.
Yes this is our first time travelling to Italy. I do wish we could have fit in the Almalffi Coast as well, but do not feel there is time with all the travel. Idea's??????

Mary, you are right, save the Amalfi Coast for the next trip.

Jeff, gorgeous photos!