You've mentioned the word "safe" in your posting 3 times so let me assure of a couple of things:
1. The L.A. metro area is safe -- among the safest 'big cities' in the U.S.
2. The lovely contributors on this Forum don't recommend hotels in dangerous neighborhoods. Nor do they recommend dirty hotels.
3. The same, safe neighborhoods are recommended to everyone -- whether you're bringing teenage girls with you or you're a Kung Fu fighter. Everyone, no matter their age or gender, is entitled to a safe place to stay.
Although I live in West Hollywood, I'm not a big fan of the Sunset Strip for families with children. It's not dangerous and, in fact, it's a pretty area with lots of the hotels having views of the city and there are also northward views of the Hollywood Hills, above. But. the Strip is primarily a nightlife area for 'grown ups' -- 'better' restaurants (except for Carney's Hot Dogs), bars, lounges, small 'concert venues'. On the weekend, it's packed with automobile traffic and pedestrians lining up in front of bars -- the men in their mandatory black shirts and black jeans and the women in their short skirts and heels.
None of this will emotionally scar your daughters but to be honest, there's little here for them unless they want fine dining, a gastropub/restaurant in which to have dinner, a trendy bistro with expensive food or high-end boutique shopping. In addition, because of the abundance of large hotels, you'll need to wade through the 'sidewalk traffic' around these hotels which have circular driveways packed with cars and taxis rushing in and out to pickup and drop off guests. This makes walking along the Sunset Strip frantic, at times and also slow-going since you have to make your way past these hotels before you can reach neighborhood restaurants.
Staying just off the street at one of the 'suite hotels' (which used to be apartment buildings and were converted to hotels to avoid rent control) will take you a little bit away from the activity on the Strip but will also make your walks even longer to area restaurants -- and, the walks will be uphill since the topography is down-sloped at this point.
A third vote for the area locally known as "Beverly Grove" which is bounded on the west by the BEVERLY Center Mall and on the east by the GROVE. This is what Yoga meant when she referred to "West Hollywood around 3rd St" (in reality, this area isn't in West Hollywood, it's in "Beverly Grove" which is in the city of L.A.)
There are several nice things about the area that would make it great for you:
1. There are no night clubs and no 'stand alone' bars here (although some restaurants have bars within them). As such, there are no masses of people lining up on the sidewalk waiting to get in and out of venues.
2. The neighborhood is flat, and easy to navigate: 2 parallel streets (3rd St & Beverly Bl bounded by the Beverly Center Mall at the west (which is on La Cienega Bl) and the Farmers Market/the Grove at the east (which is on Fairfax Av).
3. Lots and lots and lots of dining options of all kinds and in all price ranges including Chipoltle ('better' fastfood Mexican food), SoupPlantation (all you can eat soup/salad place), Dupar's (inexpensive coffee shop at Farmers Market), Johnny Rockets (hamburger place at Farmers Market), Joan's on Third (European-style deli) to mid-range restaurants like Morel's (French Bistro at the Grove), Marmalade Cafe (at Farmers Market), Calfornia Pizza Kitchen and P.F. Changs (street level at the Beverly Center). And, these are just a tiny sampling.
4. The area is extremely walkable since there is a minimum of large hotels (they're at the ends of the neighborhood) so you don't have large driveways to cross -- just shops and restaurants to explore.
5. The area is centrally-located -- just to the east of Beverly Hills which is the very CENTER of the L.A. metro area.
6. There is regular public transit here along all 4 boundary streets: Beverly Bl (the #14 bus), 3rd St (the #16 bus), La Cienega Bl (the #105 and #705) and Fairfax Av (the #217, #218 and #780). As a result, you can zip from one end of the neighborhood to the other in just a few minutes so, for example, if you stay at the Farmers Daughter near Farmers Market/the Grove, you can eat at Grand Luxe Cafe at the Beverly Center by jumping onto either the #14 or the #16 and you'll be there in 5 minutes or less.
7. There are a number of tourist attractions in the area within walking distance, a short drive or a short bus ride. These include:
a. The Grove/Farmers Market
b. CBS "Television City" Studios
c. the Museums on Wilshire Bl (LACMA/county art museum, the La Brea Tar Pits, Petersen Automotive Museum) -- all reachable via the #217 or #780 buses along Fairfax Av (3 minute ride or you can walk in about 15 minutes).
d. Rodeo Drive/Beverly Hills (15 minutes on the 16, 316 -- the 'express version of the 16' or the 14 bus).
e. Hollywood (the #217 or #780 northbound on Fairfax) -- 15 or 20 minutes.
If you buy a 'DAY PASS' for each of you for $5, you'll save on parking fees and hassle to go to these places. (The museums charge $8 to $10 to park, Hollywood can cost between $2 -- for 2 hours) to $10 to park, etc).
The hotel rating and booking section of Trip Advisor for L.A. has been under repair for almost a year, so searching for hotels in Beverly Grove is difficult (ordinarily, you can select the neighborhood called "Central L.A." on Trip Advisor and it takes you right to this area. But right now, it doesn't so, I'll do a search using map boundaries and highlight the area for you).
Click the link below and SCROLL DOWN for a map and below that, a list of hotels in Beverly Grove. The hotels are ranked by 'customer preference' (the highest in the list are 'most preferred' by travelers -- not because they are the most luxurious but, rather because the visitor was PLEASED with the experience). So, a simple hotel might appear higher in the list than a more luxurious one.
The map shows an expanded area -- a little bit outside of the boundaries of Beverly Grove. This is good because there are a few hotels I'll recommend that are just outside of the neighborhood:
a. The first three in the list are 'can't lose' places. They were picked by travelers as the best of Beverly Grove and I agree completely. They are, however, not cheap -- but also not expensive. They include:
i. Elan Hotel (bare-bones 3-star -- no amenities (no restaurant, bar, room service, bellmen, etc) but the decor is a little bit nicer than a basic 3-star.
ii.Sofitel (4-1/2 star full-service hotel and spa). If this interests you, it's often 'on sale' at Hotwire.com. Tell us your travel dates and we'll check for you.
iii. The Orlando (Yoga's pick). This is a boutique-style hotel like the Elan but it has more amenities (pool, restaurant, bellman). It's also across the street from the new Magnolia Bakery (yum) with homemade cupcakes (I like the red velvet) and blondie brownies, lemon bars. Never mind: your family probably isn't interested in that.
b. If you want to save a little money and are willing to go for a 2-star hotel (remember, these aren't 'broken down' or dirty'; they're just 'plain jane', ordinary. Here's a couple I would recommend which are 'a little bit away' from the center of Beverly Grove (5 to 7 minute walk or 1 minute drive):
i. The Wilshire Crest (the #6 hotel in the list). This hotel offers free parking (you park on the street -- a rarity in L.A. but this is a 'permit parking' neighborhood and the hotel will provide you with a permit for your car).
ii. Park Plaza Lodge (the 9th Property in the list). This hotel is EAST of the Grove but still on 3rd St (a 7 minute walk to the Grove). Free parking and cheap! You might be concerned that this is the 9th highest-ranked hotel in the neighborhood but read the reviews (of all of these hotels) and check the prices by clicking on the 'show prices' button which will bring you competing offers on this property. And, note that the hotel is rated #83 out of the 301 hotels ranked by Trip Advisor in L.A. putting it in the top 1/3 (almost the top 1/4) so given that it's a 'budget hotel' that's a pretty good accomplishment.
Hope this helps. I'm so hungry from typing I'm heading over to the Magnolia Bakery for lunch. I think I'll have a lemon bar AND a red velvet cupcake!