We stayed in this neighborhood for a month this summer and it was lovely! Paris is a big city but this is a "real" Paris neighborhood with beautiful buildings, great restaurants, and several interesting features.
Treat yourself to dinner at Le Train Blue, right inside the Gare de Lyon. Gorgeous Belle Epoque era restaurant with every original feature still intact...pricey but WELL worth the experience. You'll see it as you exit the train when you arrive.
About a 5 minute walk from the station is the Viaduc des Arts, the lower level of an old, disused, raised rail line that houses artisans and craftsmen. It's a beautiful use of abandoned space that is very interesting to browse...30 - 40 shops tucked into the old archways.
The space on the top of the viaduct is a beautiful, long, narrow garden that is similar to the high line in New York City. We walked it almost daily and enjoyed the plants and the quiet in the middle of the city. A previous posted indicated that it would not be good to visit at night but it's actually closed at sunset so that isn't possible anyway. There are groups of school kids, joggers, and residents enjoying the garden all throughout the day - it is safe and peaceful. If you keep walking north to the end, and exit down the stairs, you can keep going in the same direction and in just a few minutes be at the Bastille and a beautiful canal that is an offshoot of the Seine.
There is another wonderful, tiny restaurant on the Rue de Charenton, about a 10 minute walk from the station called L' Alchemiste. You need reservations but it is a very typical neighborhood restaurant that changes its menu daily based on available ingredients. Very good food and personal service. Super French!
I agree with several other posters that St. Denis is well worth the metro ride...yes, the neighborhood is a bit rough but the cathedral is literally a 2 minute walk around the corner from the station and the square in front of it is quite nice. Personally I think it's one of the best cathedrals in Europe for it's history, unique features, and a crypt that belongs in a movie!