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.