Recommendations for a camera & more bag

Baggalini has some cross-body bags that might be a good size for you. Check out this one. I have one very similar to this, and it works well.

Go to eBags.com and check out messenger bags and travel handbags.

I've also seen a nice-looking bag at Target made by SwissArmy that might work for you. And check out REI.

Lately I've been using the lowepro passport sling bag and have to say I really like it. Now, to be honest, it doesn't hold a ton and it is a camera bag- but that's ok since I knew I'd have to economize to carry the DSLR around all day. I could fit my canon 7d, a 15-85mm lens, extra card and batteries, small wallet, sunglasses, kleenex, small water bottle, cell phone and small pouch with lip balm, sunscreen, advil, nail file, bandaids, etc., etc. The insert that comes with it attaches via velcro so I'd stash my wallet between the insert and the side of the bag. With the exception of the water bottle, everything else fit in front of the insert.

Not terribly stylish, but it was comfortable to carry crossbody and I could hitch it up and wear it backpack style for hiking through the Highlands. I found the balance of the bag worked for me and had no trouble getting on and off small boats with it.
For London and Paris, you may want something a bit more stylish - Lo and sons makes a nice bag as well as Kelly More and Epiphany.

So I usually put a camera bag inside my personal carry on. I do that because personal carry on items are rarely set up for cameras. So here is the question..... extra lenses? I ask because when I take something like the Sony RX10 III, I have lots of extra room in the bags I use as my personal item (because the camera bag will be fairly small.) When I take the Sony AFR-II with a couple of lenses, the camera bag takes up a chunk of my personal carry on. If you only take one lens, (a camera about the size of the RX10-III) I would recommend something like a very simple camera bag which you can take without the personal bag or put it in the personal bag. When traveling the extra protection is wonderful (virtually 2 layers of padding.) If more than 1 lens, I usually will take my personal bag but remove my camera from the camera bag beforehand. The two bags I like best (although I use others for different trips and amount of equipment etc.) are the RS Veloce Shoulder Bag or Red Oxx Gator. Again, with me, I travel with the smallest camera bag I can inside my personal item but carry either the camera bag or my personal item with camera bag removed when I am shooting (depending on the size of the camera.) Good luck. While this may seem a cumbersome or unwieldy system to some, it works for me after many years of trial and error with various amounts of camera equipment and travel styles. I hope you find your own system soon.

Lauren,

I normally carry my DSLR in the open, as it's a darn nuisance to have to take it out of a bag every time I want to take a picture. If you'd prefer to use a bag, you might have a look at the line of products from ThinkTank Photo. They were designed by photographers for photographers - https://www.thinktankphoto.com/pages/shoulder-bags

They have an extensive line of products to fit just about every need.

Tom Binh offers a bag with camera insert and pockets on each end for extras.

Another vote for Lowpro bag. My husband carries his video camera in this and it also expands to hold his other stuff like an umbrella and water bottle.

https://www.amazon.com/Lowepro-Passport-Sling-III-Protective/dp/B00J938IWG/ref=sr_1_14?ie=UTF8&qid=1490743719&sr=8-14&keywords=lowepro

For an actual camera bag for DSLR plus extra lenses, I prefer this Case Logic. Great support and ease in carrying.

Thank you to everyone who replied! I hadn't come across Think Tank Photo before and now I'm debating between a Lily Deanne bag or an Urban Approach bag.

Thank you to everyone who replied! I hadn't come across Think Tank
Photo before and now I'm debating between a Lily Deanne bag or an
Urban Approach bag.

Lauren, I am a camera bag junkie. I have the small (Lucido) Lily Deanne bag from ThinkTank, and I have been happy with it for two Micro 4/3 bodies, each with f/2.8 zooms, and a full size external flash. The bag is remarkably lightweight and comfortable for the amount of stuff it carries. I used it at Carnival in Venice in February, and it served me well. Like all ThinkTank products, it is sturdy and well-designed.

The Lily Deanne a little big for me for everyday use --- my usual preference is a Billingham Hadley Small, but when I need more room the Lily Deanne is my top choice.

The LowePro Passport Sling is a nice bag that you can fold up and stash in your suitcase. I find it nice for one body and a small lens, with plenty of room left over for "purse" items. The two drawbacks are: (1) it is not at all waterproof, and (2) it gets uncomfortable if I overload it.