CHill, doubtless your hotel is much cheaper than being on the island, and if this is an issue, no biggie, but you really do lose out being on the other side. I'm not going to be snobbish about it, just want to point out how really, truly walkable Manhattan is.
An hour's walk from Midtown/Grand Central going south will take you to Wall Street, 50 minutes and you're at the Guggenheim. We have friends in SoHo and the Upper East Side, so we've done both the walks many times, and I can really recommend seeing the place this way. It is just unbelievable how much is packed in two hours walk in this place, without the pain that comes from hiking up and down hills as you would have to deal with out here. If you enjoy seeing by walking, there are few places better than NY.
Manhattan is also unquestionably one of the most expensive locations for hotels on the planet. And what you get is (mostly) small. But the weather might get sucky, and you might be stuck at or close to your hotel, and if so being on the island is just going to make all the difference.
And, for all the love I have of the drinking holes in my town, and my local, Alembic, above all, I have to hand it to NY, it has a ridiculous, spectacular number of great bars. Too many to even start on. Not gonna bother to list a bunch of out of the way places, as especially when you have little time, you aren't too likely to hack it out of the way to find a watering hole except if that's your main reason for visiting. I'll mention the Campbell Apartment as it's "in" Grand Central, tucked away on a side near the Vanderbilt Avenue portico, and not accessible from the main station, so not really in the station. Used to be the offices of John Campbell. Since Grand Central is a place you might want to visit, make it so that you can stop by and have a cocktail. Popular with locals/commuters, so crowded on a weekday afternoon, very pleasant on the weekends.
Not the sort of place that is likely to have new and inventive drinks incorporating home made citrus extracts etc etc, but a grand space, very old school, the place you would really want to order a Manhattan in.