Hi, Claire89,
I have an answer for you regarding Aberdeen - The Codona Amusement Park does have a dedicated car park. As of this past summer, it's still free to park there. The car park entrance is behind the restaurants at the far (south) end of the complex.
If you're coming from town, you can take Beach Boulevard as far as Links Road. The boulevard is closed from Links Road to the Esplanade. You can either turn right at the traffic light on to Links Road, and follow it past the shopping center on your right to the roundabout at Wellington Road. The entrance to the car park is the first left off of the roundabout.
If you turn left at the traffic light on to Links Road, you would follow it around to the Esplanade, turn right off of the roundabout, then bear left at the traffic light on to the beach front. There is angled parking along the beach front (if you can find a space!), but if you're planning to spend time at the arcades and rides, you'd be better off in the car park. Turn right at the roundabout at the end, by the Burger King, then go 3/4 of the way around the Wellington Road roundabout into the car park.
If you go that latter way, you'll be passing the Beach Ballroom, which will be on your left. The Beatles played there on January 6th., 1963, to a very small audience. Little did anyone know!
As far as getting to the beach from your hotel, it is walking distance, although you'd be walking through a heavily trafficked industrial area. There is one bad crossing for pedestrians. If you do decide to walk, turn east on Guild Street, which becomes Virginia Street. Cross over Commerce Street to Castle Terrace, then bear left on Cotton Street and follow it to Links Road. By going this way, you'll see why Aberdeen has been named the third most depressing place in which to live in Britain! You can also drive this way, if your hotel is near the train station. However, be very wary of dedicated bus lanes, which will affect you if you're driving on Guild Street. Also be aware of them if you are driving up to Union Street. The bus lanes are noted by markings on the road surface and blue street signs on the kerb (curb).
If you decide to take the bus, I think that First Bus number 13 runs from Union Square to the beach.
If you're visiting Fittie, you can park at Porca Quay, or you can park along the Esplanade between Queen's Links (where the Burger King is) and Fittie itself. Or you could even continue to park at the arcade.
As far as things to see and do on the way from Inverary to Glasgow, I'd recommend stopping at the village of Luss. Because of the heavy influx of visitors, you now have to pay to park there. It's a very attractive village, and you can walk along the pebbled beach on the shores of Loch Lomond. There are also boat tours of Loch Lomond from the pier at Luss. Reservations are pretty much a requirement. I think that there are 60 and 90 minute cruises. Personally, I'd go for the 90.
Best wishes, and Happy New Year!
Mike (Auchterless)