You will be able to travel easily along the coast from either Nice or Villefranche, the difference being that there are direct bus routes from Nice to the mountain villages of St. Paul de Vence and Eze. The 04 train route runs along the coast, so access is available from all of the resorts along the coast. In fact, for convenient access to the train station, I would prefer Villefranche. Depending upon where you are staying in Nice, you could have a further walk or need to travel by bus, tram or taxi to the train station. Nice is just a bigger city and more spread out, but it's all doable and some travelers wouldn't stay anywhere else. From your choices, I just prefer VF, but that's me and you will know what works for you.
I am so partial to the Hotel Welcome because of the wonderful experiences we've had there, especially with the very pleasant and helpful staff. I've written reviews on this topic, so I won't say more than there is nothing like sitting in your room's balcony at night, enjoying the beautiful view of the harbor and Cap Farret and enjoying a bottle of the region's Provence rose. The comings and goings from the yachts is always entertaining. I haven't stayed at the Darse, but I would expect the experience to be similar.
A taxi from the Nice airport is going to be around 70 Euros, but that started to sound cheap after my husband was pickpocketed at the Nice St. Augustin train station. This is closest station to the airport, and being jetlagged, that contributed to our vulnerability. That's not going to be the case with you, so you will probably fare better than us. As SelkieNice, Nice's Destination Expert, has pointed out, we should have bought our train tickets at the Nice airport rather than the train station. I would suggest you do this and not show your wallet at the station. This is how we found our way from the airport to the St. Augustin station, and should you decide to do this, you'll be fine if you keep your wits about you and look out for each other:
tripadvisor.com/ShowTopic-g187216-i137-k4842…
Here is how I find my way from the bus stops and train stations to the parts of the towns I want to visit. Destinations here include Cannes, Le Cannet, Nice, Antibes, Villefranche, Eze, and St. Paul de Vence>Vence>Tourrettes sur Loupe:
tripadvisor.com/ShowTopic-g187216-i137-k4846…
...and this is from this year's trip and was a lovely day's outing with my daughter. We from Villefranche through Beaulieu sur Mer and took buses to Eze Villlage and Monte Carlo. This was her favorite day on our six day trip:
tripadvisor.com/ShowTopic-g187216-i137-k5935…
I'm with datthecoast is saying that I love (all) of the resorts along the coast for different reasons and you will decide on the one that works best for you.