Oh geez....shouldn't have gotten me started on this one....I have a ton of recommendations of where to go but none as specific as "a good seafood place near Covent Garden". There are a few pubs, where you can get some wicked fish & chips, that I would recommend though:
Lamb & Flag Pub (my favorite of the bunch)
33 Rose Street (at Garrick Street)
Tube: Covent Garden/Leicester
Dicken's Inn Pub St. Katharine’s Way (off E. Smithfield)
Tube: Tower Hill
Walkers of Whitehall Pub Craig’s Court (off Whitehall) – Monday-Friday Lunch & Dinner
Tube: Charing Cross
Pluogh Pub 27 Museum Street (at Little Russell Street)
Tube: Holborn/Tottenham Court Road
Coach & Horses Pub 29 Greek Street (at Romilly Street)
Tube: Leicester Square/Tottenham Court Road
Sherlock Holmes Pub 10 Northumberland Street (at Northumberland Avenue)
Tube: Charing Cross/Embankment
I would say that you HAVE to go to
Covent Garden Market. You could spend all day just shopping around and eating here:
At Russell Street, Henrietta Street, Southhampton Street and James Street
Tube: Covent Garden
Speaking of markets...oh man...my all-time favorite market and all-time favorite meal was here (fresh rosemary bread loaf, fresh figs and farm-made sharp white cheddar horseradish cheese picked to bits while sitting at a cafe along the street).
Borough Market Southwark Street SE1 – Friday: 11AM-6PM; Sat. 9AM-4PM
Tube: London Bridge
Also near here that you should see is the Globe Theatre, London Tower and Tate Modern is close.
There are SO many good markets to go to:
Shepherd Market Between White Horse Street and Trebeck Street
Tube: Green Park/Hyde Corner Park
Berwick Street Market Between Peter Street and Broadwick Street – Monday-Saturday 9AM-3:30PM
Tube: Piccadilly Circus
Camden Town Market Camden Lock Place (off Chalk Farm Road) - Thursday-Sunday
Tube: Camden Town
Smithfield Market (huge!!! and a most stop)
Bounded by Lindsey Street, Farringdon Road, W Smithfield and Charterhouse Street – M-F 5AM-10:30AM
Tube: Barbican/Farringdon
Berwick Street Market (tons of fresh fruit and veggies, maybe slow this time of year though)
Between Peter and Broadwick Streets – M-Sa, 9AM-3:30PM
Tube: Piccadilly Circus
Spitalfields Market (very big and a lot of stuff)
Bounded by Brick Lane, Bishopsgate, Middlesex, Whitechapel High and Quaker Street – Sa-Su
Tube: Liverpool Street
Brick Lane Market (in a weird area but tons of street food...and flea market type stuff)
Liverpool Street, Aldgate East, Old Street – Sun, 6AM-12PM
Tube: Liverpool Street
Leadenhall Market (lots of farm fresh stuff, cheese, eggs, etc)
Gracechurch Street (between Fernchurch and Leadenhall Street) – M-F
Tube: Bank/Monument
Billingsgate Fish Market (if you like seafood...this is a must, it's crazy...it's were London buys their fish...it's HUGE)
Lower Thames Street – Tu-Sa, 5AM-8:30AM
Tube: Bank/Monument/Central/Northern/Waterloo/City
You have have have to go to
Harrods, it's a gigantic department center. The first (of 7) floor houses a huge market with literally every type of food you can possibly imagine...it is a foodies dream, you must go here. Also this time of year is perfect, they have an enormous Christmas space....and their toy department is unrivaled!
135 Brompton Road (between Hans Crescent and Hans Road)
Tube: Knightsbridge
Other foodie stops:
Paxton & Whitfield (tons and tons of cheese)
93 Jermyn Street (between Duke of York and Duke Streets) – Monday-Saturday
Tube: Green Park/Piccadilly Circus
Fortnum & Mason (everything rich you'd want...caviar, truffles, marrons glaces, hand-dipped chocolates, Stilton cheeses, teas, honeys, Champagnes and foie gras)
181 Piccadilly (at Duke Street)
Tube: Green Park/Piccadilly Circus
Ye Olde Cheshire Cheese (cheese and cheese!)
145 Fleet Street (between Shoe Lane and Hind Court) – Bar: M-F, 11:30AM-11PM; Sa, 12-9PM; Su, 12-3PM
Tube: Blackfriars
Comptoir Gascon (tons of French items)
61 Charterhouse Street EC1 – M-F, 8AM-8:30PM; Sa, 10AM-5PM
Tube: Farringdon/Barbican
....and if that wasn't enough for you...here are some of my top destination aside for the usual Westminster Abbey, Tower Bridge, London Eye, House of Parliament, etc (although I highly recommend them all too):
Kensington Palace (absolutely beautiful)
Palace Avenue (off of Kensington Road)
Tube: High Street, Kensington
Kensington Gardens (gorgeous)
Bounded by Park Lane, Palace Avenue, Knightsbridge, Kensington Road and Bayswater Road
Tube: South Kensington/Marble Arch/Hyde Park Corner/Knightsbridge/Lancaster Gate/High Street Kensington/Queensway
Victoria and Albert Museum (one of my all-time favorite museums in the world...you could spend a month here)
Exhibition Road and Cromwell Road – Free – Daily 10AM – 5:45PM
Tube: South Kensington
The British Museum (tons of history)
Great Russell Street (between Montague and Bloomsbury Street) – Free – Sa-W, 10AM-5:30AM; Th-F, 10AM-8:30PM
Tube: Russell Square/Holborn/Tottenham Court Road
Tate Modern (I love this place)
Near Shakespeare’s Globe and Thames – Free - Su-Th, 10AM-6PM; F-Sa, 10AM-10PM
Tube: Blackfriars/Waterloo/London Bridge
....well...I know that wasn't quite what you asked for but I hope it helps and gets you started
I seriously recommend going to them all. How long is your trip? Where are you staying? Let me know if you have questions...I'll try to help.