Best Places to Visit by Public Transit early April?

You might want to take a day trip from Paris to Monet's garden at Giverny, or even overnight in the nearby town of Vernon. The gardens at Versailles are huge and legendary, also a day trip from Paris.

A longer trip could be a train to Tours, then some of the chateaux in the Loire valley by minivan. Here's one tour operator, I'm sure there are others. I haven't used them, I've driven, but several of the chateaux have wonderful gardens -- Villandry, Chenonceau, Azay-le-Rideau come to mind. You could stay 2-3 of nights in Tours and see several chateaux over a couple of full days.

Great Gothic cathedrals in Reims (to the east) and Chartres (to the southwest). Reims also gets you into champagne cellars if that floats your boat. These could be day trips from Paris or overnight if you want a more leisurely pace. Chartres Cathedral adjoins a medieval city center good for strolling, markets etc. A lot of Reims' center is post-war, the price of being located between Paris and Germany, but there's a Roman gate north of the cathedral that's worth seeing.

Or you could easily spend a week or two in Paris itself, with a few daytrips. There's plenty to see and do in the city. Have a great trip!

How will the gardens be in early April?

Here's the website for Monet's garden, including how to get there and much more. Here's a list of plants likely to be flowering there in April. Of course weather can be unpredictable, which is why it might be safest to do this as a day trip whenever the weather looks favorable, instead of locking yourself into a day far in advance.

If you're looking for cities different from Paris, you could visit Lyon for 1-2 nights, or take a 2 day trip to Strasbourg and Nancy (day 1 Strasbourg, overnight in Strasbourg, day 2 train to Nancy, that evening return to Paris). These trips are less than 2 hours each way by TGV, and the tickets are not expensive if bought far enough in advance (non-refundable).

Lyon is my favorite city in France outside of Paris. On certain days there's a very large farmer's market all along the banks of the Rhone. There's also lots of other things to see there, from a Museum of the Resistance (which also has materials on collaboration), to Roman artifacts, to the museum about the Lumiere brothers (early photography pioneers). Rick's France book has a good chapter on the city.

I wasn't as taken with Strasbourg as some, but I loved the Museum of Alsatian Life. And Nancy is an undiscovered gem (the only one of the three cities not in Rick's France book), with lots of great Art Nouveau architecture and amazing glassware.

"I love art, architecture,gardens, hours of walking and checking out the street scene, farmers markets and that sort of stuff."

+1 for Lyon, we loved it there. It's like a digestible sized Paris. Off the charts food opportunities.
Here's my Lyon Gallery from September:
http://thecedarchest.smugmug.com/Lyon-2014/

Keep in mind that April 5 is Easter Sunday and may impact some of your plans. As an art lover, you may not want to leave Paris at all . . . the art museums are numerous and one is better than the next.

There are literally dozens of great day trips from Paris. Within an hour of Paris you can visit Giverny, Reims, Rouen, Crecy la Chapelle, Senlis, Auvers sur Oise, Chartres, Versailles, Chateaux at Rambouilet, Vaux le Vicomte or Fontainebleau -- and many others. I'd base in Paris which is a great place for singles and has so many great things to do and plan a few day trips. Take a look at some examples in my photo journal -- www.janettravels.wordpress.com -- and there are many others. And within Paris itself there are so many neighborhoods to explore --

Have a great trip.