Fronting the northern end of Trafalgar Square are the city's expansive national collections of art and portraiture. Don't miss Van Gogh's Sunflowers or Botticelli's Venus and Mars at the National Gallery (WC2, 020-7747 2885, nationalgallery.org.uk). Then wend your way chronologically through hundreds of familiar faces at the National Portrait Gallery (St Martin's Place, WC2, 020-7306 0055, npg.org.uk), or check out its exhibition of 60 years of images of her Maj. Stop for a grand afternoon tea at the Wolseley (160 Piccadilly, W1, 020-7499 6996, thewolseley.com), impressively set in a former Bentley showroom. Then spin through the eclectic Summer Exhibition at the Royal Academy of Arts (Burlington House, Piccadilly, W1, 020-7300 8000, royalacademy.org.uk), now in its 244th year. Runs until 12 August.
Ease into your day, listening for whispers at St Paul's Cathedral (EC4, 020-7246 8348, stpauls.co.uk) before descending through its wonderful layers to the tomb-filled crypt. Hop over the Millennium Bridge to discover Tino Sehgal's Turbine Hall at Tate Modern (Bankside, SE1, 020-7887 8888, tate.org.uk/visit/tate-modern). Stroll down the river to the piles of artisan produce at Borough Market (corner of Southwark Street and Stoney Street, SE1, 020-7407 1002, boroughmarket.org.uk), and, for something a little more curious, seek out the narrow staircase up to the Old Operating Theatre (9a St Thomas's Street, SE1, 020-7188 2679, thegarret.org.uk) for a gruesome glance at 19th-century medical practice.
Start boldly with a gallop through antiquity at the British Museum (Great Russell St, WC1, 020-7323 8299, britishmuseum.org), which offers plenty of tours for the short-of-time. Pause for a look at the scale model of the capital and its most recent developments at the Building Centre (26 Store St, WC1, 020-7692 4000, newlondonarchitecture.org) and then drop in at the diminutive Newman Arms (23 Rathbone St, W1, 020-7636 1127, newmanarms.co.uk) for a pie and a pint. Finish with a stroll up Gower Street to the Wellcome Collection (183 Euston Rd, NW1, 020-7611 2222, wellcomecollection.org), a treasure trove of life in all its messy glory.
The ceremonial unlocking of the Tower of London (EC3, 0844 482 7777, hrp.org.uk/toweroflondon) at 8.45am is an excellent daily introduction to its unique blend of history and tradition, and a Yeoman Warder's tour provides a hugely entertaining insight into this mighty fortress. It's an irregular schedule, but try to catch Tower Bridge (SE1, 020-7403 3761, towerbridge.org.uk) opening its great arms, or pop inside for walkway views and an illuminating look at its revolutionary mechanism. Then check out the Wine Library's (43 Trinity Square, EC3, 020-7481 0415, winelibrary.co.uk) well-stocked cellar before a wander west, where a climb up Wren's Monument (EC3, 020-7626 2717, themonument.info) rewards you with a fantastic panorama as well as a certificate to mark the achievement.
For something more bucolic, head west to Chiswick and the recently reopened Hogarth's House (Hogarth Lane, W4, 020-8994 6757, hounslow.info/arts/hogarthshouse), a beautiful restoration of the painter's home. Just behind lies Chiswick House and Gardens (Burlington Lane, W4, 020-8995 0508, chgt.org.uk), a sumptuous neo-Palladian villa set in glorious surrounds. The pretty riverside walk at Strand on the Green, not far to the south-west, sports a little row of pubs perfect for an alfresco drink. And up the towpath and across the water lies the vast expanse of Kew's Royal Botanic Gardens (TW9, 020-8332 5655, kew.org), boasting historic hothouses, elegant architecture and a popular arboretum and treetop walkway.
Sally Schafer co-wrote the Lonely Planet London city guide (?14.99). For Lonely Planet's free downloadable guide to Stratford and east London, see lonelyplanet.com/campaigns/london/2012