If you're planning a trip to Scotland, keep in mind Shieldhill, a country-house hotel that offers solace in the peaceful Clyde Valley between Edinburgh and Glasgow. A hideaway for honeymooners, young marrieds--or anyone else seeking tranquillity in a woodsy, garden-like setting. Proprietors Jack Greenwald and Christine Dunstan, who launched the highly successful Cheshire Cat B&B in Santa Barbara, are welcoming friends/former guests at this refurbished Scottish manor. Dates from 1199. King, queen, four-poster beds, log-burning fireplaces, Laura Ashley trimmings, color TV, hair dryers, gourmet meals. Golf nearby and salmon fishing on the River Tweed. One of Scotland's best-kept secrets.

Shieldhill Hotel, Quothquan, Biggar, Lanarkshire ML12 6NA, Scotland (roughly midway between Edinburgh and Glasgow). Call 0899-20035. Rates: 79/119 (about $150/$226) double, including a Scottish breakfast and value-added tax.

Illinois Guide: Illinois has produced a new visitors guide. This is a slick 240-page book containing excellent photos/maps, information on visitor centers, parks, beaches, museums, river cruises, bicycle trails, the Land of Lincoln, theaters, sightseeing, festivals/events, antiquing, entertainment, transportation. Describes scenic drives around Lake Michigan and along the Great River Road. Divides the state into seven areas. Forty pages devoted to Chicago alone. Packed with helpful details.

For free copies, call (800) 223-0121 or write the Illinois Bureau of Tourism, P.O. Box 7905, Mt. Prospect, Ill. 60056-7905.

London/Paris: An eight-day London/Paris package offered by British Travel Associates is still getting raves. Begins in London, with three days in Paris and a return to London. Labeled "a tale of two cities." Price: $77 per day. A choice of 24 hotels with private baths/breakfast. Transportation by BritRail, French Railways, hovercraft via the English Channel. This package comes with unlimited transportation on London/Paris underground/bus systems. Other bonuses: discount vouchers for sightseeing/shopping/dining, plus free street maps. Valid through March 16, 1991. Travelers are urged to book at least 21 days before leaving the United States. Contact British Travel Associates, P.O. Box 299, Elkton, Va. 22827, (800) 327-6097.

Meanwhile, beginning Oct. 1, BTA will offer its London Explorer package at the same $66-a-day price for the third consecutive year. Besides hotels, the package includes a day-trip to Canterbury, discount vouchers, passes on underground/double-decker buses, transfers between Heathrow and Gatwick airports. Details from BTA at the above address/telephone.