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and safety-wise which place is better NJ (near Lincoln tunnel) or Brooklyn?
Williamsburg or Brooklyn Heights (near brooklyn bridge) ?
It depends. Most NJ-side locations are fine, though there are cheaper hotels on the 1/9 for example that are very seedy. Many people stay around MetLife Stadium (e.g. in Harmon Meadow or on Paterson Plank Road), both have buses nearby. Jersey City also has some nice hotels near the water, which have the Path nearby, which is very fast into the city.
Note it will be extremely difficult to find a hotel in the MetLife Stadium area if you're coming in late January/very early Feb (around the Super Bowl).
Brooklyn widely varies, Brooklyn Heights is likely the safest, while Williamsburg depends on the North vs. South side (both are relatively safe, though as a tourist I'd feel better on the north side).
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and If I decided to stay in Manhattan then LES ?
LES is mostly safe, though late at night as a tourist I could see yourself feeling uncomfortable on the far east or south side of the neighborhood.