The Ashmolean Museum, Beaumont Street. An extraordinarily rich collection of historical artifacts and works of art: Britain's oldest public museum. Forthcoming relevant talks: 'Introduction to the Indian Collection' (Dec 8), 'Baroque Art' (Dec 21) - details here.
Early Modern 'Drug Trade' online exhibition from the Museum of the History of Science.
Pitt Rivers Museum, Parks Road (access through the Oxford University Museum of Natural History). Rich, esoteric, anthropological collections of (mainly non-European) weapons, sculptures, ceremonial items and shrunken heads. The Research Centre for Musical Instruments and Textiles is on Banbury Road.
Christ Church Picture Gallery, Canterbury Quad, Christ Church (acces from Oriel Square/Merton St). Superb collection of 'Old Master' paintings and drawings, including works by Durer, Tintoretto, Veronese, Rubens, Leonardo, Michelangelo and Raphael. The gallery is small but the large collection is on regular rotation.
The Museum of Oxford, St. Aldate's: limited early modern content, but good for the development of the city and University.
Botanic Gardens, High Street/Magdalen Bridge. Fascinating in its own right, of course, but also notable as a product of sixteenth-century scientific enquiry. The oldest plant, an Austrian black tree, was planted in 1795.