The main route into Scarborough from Yorkshire and the south is the A64 from Leeds and York - a trunk route with a mix of dual- and single-carriageway, it can get very busy during the summer and at weekends. The quickest route is to turn off at the Bridlington junction, then take the scenic route towards Bridlington. The scenery is stunning and will definitely not disappoint.
Other routes are the A170 from Thirsk and Pickering and the coastal routes--the A165 to the south, from Hull and East Yorkshire, and the A171 to the north, from Whitby and Teesside. Again, heavy traffic can be a problem.
Although there is plenty of parking in the town centre, it can get filled up quickly during the summer, and if you are visiting just for the day, you may find it easiest to use the Park and Ride at Weaponness, clearly signposted as you approach the town centre.
A daily, continuous Park and Ride service operates throughout the year from two sites, one on Filey Road for traffic from the south and the second on Seamer Road for traffic from the west, see National Park and Ride Directory 
TransPennine Express  run an hourly fast train service to York, Leeds and Manchester, with onward connections to the rest of the country. Northern Rail  run a less frequent service down the coast to Bridlington and Hull.
For passengers on a budget, National Express  run a coach once daily from London.
Coastliner  run an hourly bus to York and Leeds (timetable for 843 ), and EYMS  run an hourly bus to Bridlington and Hull (timetable for 121 ). These are slower than the train services, but are cheaper.
Some of the attractions in Scarborough are along the seafront, some are in the town centre a short walk inland up the steep main road. When you get to either area everything will be easily walkable for most people. There are regular buses  if you don't feel like walking.
Although the town is an ideal size to cycle around, much of it is quite hilly, so less fit cyclists may find it a challenge.
The Castle headland divides the coast into two bays, each different in character. South Bay is developed, and you'll find amusement arcades, a funfair, the harbour, the Spa complex, donkey rides, and all the colour of a traditional English seaside resort. North Bay, by contrast, is relatively undeveloped and is quieter.
One Day Trips from Scarborough
Rock - preferably pink with "Scarborough" written in it.
The Harbour Bar on the foreshore, South Bay, has the best icecream in town (for summer). Its fantastic, kitsch yet completely genuine 1930s ice-cream parlour and coffee shop that also serves horlicks, hot chocolate,Bovril drinks and an assortment of snacks (just what you need to warm you up after a walk on the sea-front on a cold winters day). It is restored to its original form every ten years or so at great expense.
For good fish and chips, you should try Mother Hubbards or Wackers in the town center but all the fish and chip shops are reasonably good. Cafe Fish on York Place is also excellent. Small Fry on North Street (behind the Post Office) is excellent, fries in vegetable oil, but is closed Saturday night and Sundays.
Coffee at it's best - Roasters  . Fully qualified Barista and boy it shows. mmm.. coffee
The Cask public house at the south end of Valley Bridge offers good quality meals at reasonable prices.
For a world renowned restaurant, try the Lanterna on Queen Street. Difficult to get in, but serves quality Italian food.
Florios, on Aberdeen Walk is a popular, and very busy, Italian restaurant.
Scarborough has a number of Indian restaurants, the Indian Rose on Victora Road and the Scarborough Tandoori on St. Thomas Street are two of the most popular.
Cafe Heart, at the side of the market on Eastborough offers a fabulous selection of smoothies, juices and thick continental hot chocolate along with toasties, pittas and sandwiches with a continental flavour (closed Sundays).
There are a vast number of hotels and guest houses ranging from three/four star hotels to small guest houses. Get in touch with the local tourist office and they'll send you a list.
Alternatively you could try:
If you're having an extended stay in the coastal town and it's nice weather get out on your bike and visit Forge Valley woods, or cycle part of the old railway route to Whitby.