Yes, you are in the right area, Llechwedd. If you keep walking East after the flats you will come to the start of the path in the public car park which is just below Morrisons Supermarket. It runs along the old B.R. track past Ferodo, fork 2nd left at the roundabout which leads onto the Y Felinheli bypass and then downhill past "Crossings Cottage" down to the waterfront past the boatyards in Y Felinheli, where there is an excellent pub called Y Garddfon, which serves coffee as well as beer/bar meals. It is approx.4.5 miles long and takes just over an hour or so.
It is much quieter than the Lon Eifion path which starts just past the Welsh Highland Railway station at the other end of Caernarfon and runs in a westerly direction for 12.5 miles up to Bryncir. This one is great on a bike as it has a very slight uphill gradient most of the way (not too steep as it used to be a railway track too) on the outward leg but very relaxing on the return leg!