How exciting for you!
If you haven't booked your flights and hotels yet, and you are flexible on departure and return dates, I would look into discount and last minute sites like
http://www.lastminute.com/ which can allow you to travel for a fraction of the price (depending on destinations), sometimes one third less than booking directly with the airlines... keeping an eye on them regularly before booking helps, too... because prices can fluctuate daily. Generally, on Lastminute.com, the closer to your travel time you book, the cheaper the ticket. The day of the week in which you want to travel can make a significant difference to the price as well.
Also look into if you are landing in Heathrow or Gatwick airports, sometimes you can save a lot by looking at both. Getting to Gatwick from London doesn't necessarily take longer, but if it saves you hundreds that you could use on your holiday instead, why not.
Check your airline's luggage weight allowance, and make sure you stay within it... the costs can spiral otherwise... not to mention public transportation from airports is murder with all the stairs and long walks between train switches. Might be easier to invest in a cab if you can afford it.
If you know you will not be making nor receiving a lot of urgent calls, you really don't need a sim. You can switch your phone data off (to make completely certain you will not receive surprise bills), and switch on the wifi and make free calls home to family and friends via Facetime, Skype, Google Hangouts, or whatever... texting can similarly be switched to wifi with iMessages or WhatsApp or similar apps. I'm sure your hotel will have wifi... and most bars restaurants and shops in London have wifi now... so you can check your messages when you're out and about, too...
If you feel you might need to make and receive calls, then you can have your phone unlocked, but the new iPhone system will lock itself to the new network once again, so you may need to do it a second time when you're in Paris.
http://www.tripadvisor.co.uk/ is a good app to download before you set off... it uses your location to tell you the nearest well reviewed pubs, restaurants, etc... if you find yourself somewhere without a definite plan and you want to be spontaneous, it can make a big difference to the quality you get. The reviews and descriptions are on the whole extremely reliable.
Bring your adapter plugs with you... saves you using your vacation time looking for such things... and choose the dates you switch your money from the dollar to the pound and Euro wisely, exchange rates can also fluctuate... and shop around to get the best deal, banks and airports are not usually the best offers.
You might want to call or visit your bank to let them know you may use your card overseas, some of them automatically shut down your card if they notice unusual activity... they will also inform you if there are extra charges involved in paying with your card overseas, or withdrawing from cash machines... they'll also tell you the cheapest options of accessing your money whilst there e.g. banks they are affiliated with who will not charge you. Bringing cash and transferring to local currencies in advance may be easier. Beware of pickpockets in both London and Paris, it happens a lot and they do like to target tourists... they use sophisticated distraction and diversion techniques, so do keep your wits about you without letting it distract from your good times.
If you are Californians, dress more warmly than you think you might need... layers help, it can get pretty windy here these days, so a windbreaker type outerwear will make a big difference.
Beware of hotels advertising themselves as being centrally located, sometimes zone 2, 3, or 4 hotels will tell you they are near the attractions... Ideally, what you want is zone 1 (they are zones which divide the city in concentric circles going outward)... what you're not being told is you will pay a lot in using the underground train system. Although you can get to and from those zones in minutes, you do pay for every extra zone you cross. If you are good walkers, you can see a vast majority of attractions on foot! Things are closer together than you might think, and you have more time to see stuff, rather than time spent in public transport. Any difference in hotel price should be offset by savings on travel costs.
The cheapest way to travel is an electronic tap in and tap out Oyster card... you can get this at any train station.
I hope you have a wonderful trip and the weather is kind to you!