Greenwich vs Avignon

Greenwich is lovely, feels like a little seaside town somehow, get some food at the market or fish and chips, and if time walk up to the Royal Observatory, a beautiful building and home of Greenwich Mean Time, stand on the prime meridian, and enjoy amazing views across London from the hill.

Greenwich, great for a longer afternoon wandering the market, park, historic streets and riverside without needing a strict itinerary.

I would also strongly recommend you select an apartment that has a good kitchen and dining table. ... I think a day at Greenwich would appeal to the teens

Greenwich is a good trip.

Greenwich, loads to see here, including Greenwich Park, Old Royal Naval College (free areas), and a market with various food stalls.

I've used Avignon as a home base for trips to Pont du Gard, Uzes, Arles, Saint Remy de Provence, L'Isle Sur la Sorgue, Nimes, Aix en Provence and Marseille. Those would all be 90 minutes max in each direction, and most are under an hour.

Avignon and Nice both make great bases to explore the south coast of France. One week in each

Avignon was home to the popes and has a medieval papal palace with lots of Gothic art.

Carcassonne, Montpellier, Avignon, Aix are worth visit

For a genuine sense of the south of France, Avignon is your best option if you can travel a little further. Have fun :)