I want to explore Survival Mode maps, are there ways I can do it like split screen or Team Death Match?
All the Survival Mode maps are the same maps that appear in MW3's multiplayer. If you want to just walk around the map unopposed, simply start a local game with that match and walk around. However, simply knowing the maps isn't enough - until you fight enemies on the map, you don't really get a good feel for sight lines, blind spots, flanks, etc. But yes, you can explore them on your own.
To start a local match select "Multiplayer" from the main screen:
Then select "Split Screen" (X360/PS3 only; if on PC, you're out of luck exploring the maps):
Then set up the match and you can walk around the maps at your leisure!