The entry for England is quite limited because I have traveled (so far) only to London and most of those visits have been brief. Here are a few suggestions, though, and I will add more as I have more experiences.
Where to stay in London
London is a big city and of course there are countless pros and cons to each location. I have found that the area around the Kings Cross and St. Pancras train stations is convenient as you can get to the airports and around the city relatively easily.

The Megaro – this charming and quirky boutique hotel is reasonably priced, clean and comfortable. Best of all, it offers quite a good breakfast downstairs and is literally across the street from the train stations.

St. Pancras Renaissance Hotel – located in a Gothic Revival building dating from 1873, the Renaissance is a unique treat and convenient, too.
Pullman London St. Pancras – functional and modern with top-notch service, this Accor hotel is located just two blocks from the stations. It has a nice restaurant in the lobby.
Where to eat in London
London is a great city for food. Here are places I have personally eaten and would recommend to you.
Dishoom Kings Cross – tucked behind Kings Cross station is this interesting restaurant (they have other locations but I haven’t tried those) that is basically Bombay street food served in a converted warehouse setting that is meant to evoke a 1920s godown. The food was simple but tasty. Pictured above: spicy lamb chops with grilled greens and cheese naan. For dessert, Memsahib’s Mess, a concoction of meringue, strawberries, whipped cream and rose syrup.
OXO Tower Restaurant – I ate at this modern brasserie on an early visit to London. Located on the south bank it offers a garden terrace and panoramic skyline. The food is globally influenced and the service is superb.

Kingly Court – this three-story alfresco complex in the West End features almost two dozen international food and drink options. Of particular note is the Peruvian restaurant Señor Ceviche and Calcutta-inspired Darjeeling Express. Food from Darjeeling Express pictured above.

The Harwood Arms – at the time of this writing, the only Michelin-starred pub in London, this comfortable restaurant offers set menus with locally-grown and sustainably produced ingredients. Thoughtfully made but unfussy, this is elevated pub food. Located a bit west of the main city in Fulham, easy to get.
Dumpling Shack – London might not be the first city that springs to mind when you think of places to find great Chinese dumplings. Dumpling Shack, though, will correct that misperception. Located in the happening Old Spitalfields Market (see below), they have the hard-to-find sheng jian bao, a Shanghainese style panfried dumpling that is one of the foods I would request for a last meal. Worth a visit.
Things to do in London
Of course every big city has its tourist attractions. These can be well worth visiting. Sometimes, though, I find that the best way to explore a city and get a sense of it is to visit more everyday parts of it: go where the locals go. Here are a few of the places I found that made me feel like I gathered a sense of London.

Old Spitalfields Market – there has been a market on this site for more than 350 years. It has been redeveloped in the last decade into something quite light and full of energy, a combination of boutiques, restaurants and shops giving you plenty to explore. Located in the East End, it is a short walk from Liverpool Street station.

Columbia Road Flower Market – open on Sundays only, this East London street market has a variety of interesting vendors, focusing mainly on plants and flowers. Worth a walk around and you can grab a cup of coffee and a bite to eat at a number of places in and around the market.

Walking paths by Transport London – while also being responsible for the transit in the city of London, Transport London does a great job of making the city especially accessible for pedestrians. They have mapped hundred of kilometers of walking paths and have identified seven routes that are part of the Walk London Network. On their website are PDF guides to each of the sections of those routes, making them easy to navigate and allowing you to explore different parts of London. I took the Thames Path following the river from Albert Bridge to Tower Bridge along the South Bank of the river.