Cake central, kinda pricy but good
Lets bake love by Sara Taneja.. (lajpat nagar)this is one of the bestest bakery and she does customised cakes with details
Cake centeral design studio in defence colony is a good option.
Check out @Creative_hands229 (Instagram) for best gifting options. They have wide variety & best customer service.
You'll find a lot of such places on Instagram which will be providing you home delivery as well