I will be visiting a client located in Union City, NJ for a week (arriving Monday, leaving Friday).

Looks like Union City is close enough to Manhattan (just across the bridge?). I am thinking of getting a hotel in Manhattan and just take take cabs to/from my client location everyday. Any idea how much the fare would be between Union City, NJ and either Times Square or Chelsea? I need to be at the client location at 9 AM each day. Also, is it easy to get cabs to/from Union City?

NYC yellow taxis aren't required to take passengers to NJ (except to EWR) and metered rates don't apply, so you'd have to negotiate the trip and a flat fare with the cab driver each time you hail a cab in Manhattan. NYC taxis also aren't allowed to pick up in Union City so you'd have to call a car service or local cab company to bring you back (I doubt if you can hail a cab on the street in Union City).

You might talk to the client and see if they can recommend a Union City (or nearby) based cab company or car service that you can arrange ahead of time to take care of rides both ways (I believe NJ cabs can pick up in NYC if they're dispatched and taking you to NJ). But even then I'm not sure if you want to be going through the Lincoln Tunnel at rush hour every day.

You might want to look into the Port Imperial ferry. It'll be a more pleasant and more reliable way to get across the river, and from there you can either have a cab/car service pick you up or (depending on where exactly you're going) take the Hudson-Bergen light rail the rest of the way.

I'm assuming it really is Union City, as you wrote, and not Union Township (which is farther away).

As themicah noted, fares from NYC will have to be negotiated. I imagine you would have to pay an awful lot of money to get a cab to cross the Lincoln Tunnel (and back) during rush hour.

If you start at Times Square, it is a short walk to the Port Authority Bus Terminal for buses to NJ, and this is probably the best way, especially if your destination is near route 495 (the approach to the Lincoln Tunnel) - there's some traffic but it is still scheduled at only 8 minutes from the PABT to 31st & Bergenline in Union City on the NJ Transit website, and I would guess that actual times are something like that. A ferry is a possible alternate but probably more confusing and time-consuming because of the need for travel on both ends (but it may depend on where exactly you are going). Likewise, coming from Chelsea will add some time; which way is the best will depend on where exactly you are starting and ending.

Returning in the afternoon, the tunnel is a worse bet and the balance is likely to shift toward other modes (i.e. crossing by ferry or perhaps even PATH train, rather than taxi or bus through the tunnel). To give you an idea, scheduled bus times are 25-37 minutes (compared to the 8 for the reverse trip in the morning).

Sorry if this is confusing - you should probably either talk to someone at the client site or pin down the location.

Go to NJTransit.com and enter the client address (via trip planner) and see what options are available. They will pay for a cab but doubtful any T&E wants to cover a cheap cab fare in the AM (no traffic) and 4x the cost returning to NYC at night.

Additionally, with the toll you are starting at $10 just on tolls for each trip.

Fort Lee to Chelsea is about $35-45 each way, plus tip and tolls. Union City should be in the same range. As others have said, you will have to pre-arrange for a UC car service in both directions. Most days, it shouldn't take more than 20 minutes, but if there's any sort of traffic issues, it could easily take an hour.

If you decide to take a bus, be sure to ask at your client which one. Most run along JFK Boulevard at the top of the palisades, but many industrial companies are along West Side Avenue near the rail road tracks - which would not be walkable. And some stop at every corner along the way, which could make for a very long ride.

Ask the client for commuting suggestions to/from Manhattan. That's your best bet. You won't be able to get a NYC taxi to take you back to the city as others here have said. I'm sure your client can give you some workable suggestions.