Crowne Plaza is definitely located in the best district (Gare de Lyon is mainly a soulless business district) :
located in the Haut Marais, full of trendy boutiques and restaurants (by the way, I am suprised that the hotel has not been transformed into a Kimpton hotel, as the area is definitely fits more with the positioning than Opéra, where only tourists go).

Some good spots at walkable distance from the hotel (less than 10 minutes walk) :

Season organic restaurant


Broken arm, trendy boutique


Anahi, great Argentine restaurant


Hôtel Providence, with very good restaurant (with some French stars)


Copper Bay, excellent cocktail bar


Chiche, warm and friendly Israelian restaurant


House of 3 brothers, excellent contemporary patisserie


Yann couvreur, another great pâtissier


Chateaubriand, excellent bistronomique restaurant


Candaleria, one of the coolest bar in Paris


Popelini, so chou!


PNY burger, tasty and design


Galerie Chantal Crousel, one of the most avant garde art galleries in Paris


Merci, creative concept store with a café


Maison Plisson, food to buy or to eat at restaurant


Maison Kitsuné, one of the most trendy French fashion label (with a café)


Renaissance République, with a hidden, quiet and very pleasant garden (restaurant and bar)


All the districts North (Canal Saint Martin), North East (Ménilmontant) and South of the hotel (Marais) are one of the most trendy areas in Paris.

Enjoy!