We are picking up a car in Vancouver to do some travelling around British Columbia before returning to Vancouver to travel onwards to Seattle by train. Where would be the best place to pick up and drop off the car?

Are you flying into Vancouver? Are you departing as soon as you get the car? Then pick up at the airport.
If you'll be in town for a bit, using public transport before you head off on the drive, then pick up a car close to your hotel.
Upon return, are you dropping the car off and leaving immediately on the train? Then drop off somewhere downtown, close by the train station.
You can probably pick up and drop off in different locations.
If you give a bit more info, you'll get more detailed assistance.

Yes, we are flying into Vancouver, staying in the Westin grand for 4 days and then picking the car up. Upon returning the car we will be getting the train to Seattle for a few days before flying home.We will have suitcases so we want to drop the car off as close to the train station as possible.

The Westin Grand is at the corner of Robson and Homer. There's a Budget Rent-a-Car very close by, at Georgia and Richards... just around the corner, really, about a block and a half away. That's the closest one to your hotel.
The train station is not really within walking distance from there. Perhaps a mile or so, but through a not-so-great part of town and tricky with luggage. (It really isn't in the most convenient location).
One person could drop the car off at the original pickup office, walk back to the hotel and meet the others. Then take a cab from your hotel to the train.
Or see if the hotel has, or knows of, a shuttle (unlikely but possible).

Or have you already decided on a different car rental company? They'll all have offices downtown, just not so convenient to your hotel.
FYI you might also want the car for one day of your Vancouver sightseeing if you are planning to do anything on the North Shore.

Thanks very much for the replies Taggie, they were much appreciated.Would it be any easier for us to pick the car up at the airport as we are then heading to Clearwater for a stopover before we head to Jasper. As you obviously seem to know a bit about the city, how easy is it and how long does it take to get to and from the airport.

If traffic is good the airport is about a 30 minute drive south of downtown. It just wouldn't be that convenient for you. You'd have to get out to the airport (from downtown) to get the car, then wend your way through various suburbs 9or head right back into town) in order to get onto the trans-canada highway to head east. Much easier to get onto the highway from downtown.
When you first fly in, before you get the car 4 days later, you can get one of a number of shuttles to downtown.

I kind of got the order of things messed up in my previous post. Guess you will be dropping the car off and heading right to the train without a hotel stay. Still, I think downtown is the way to go.

I'm assuming you're from the UK by your email address. Downtown Vancouver is pretty easy to navigate, basically a grid system with wide streets - nothing like London, or Cheltenham, or Edinburgh, or any of the other UK cities we've driven in (Vancouver will seem brand new to you). Although our drivers here are worse...

Cheers Taggie, thanks for all the info it will be put to good use.

Best of luck Stephen. I hope you enjoy your trip! I am heading over to the UK later this summer.
BTW, it is currently very, very dry and warmer than average here. Last year we had terrible, devastating forest fires. Many people in the B.C. interior (ie Kelowna) lost their homes. Looks as if this year could be the same. There's already a ban on campfires and our lawns are rapidly turning brown. I hope all is well during your travels here.