I know this is a difficult situation...I just went away for a few days in the beginning of December, and that was rough.
With my shih tzu, I used to board her at the vets' office. That wasn't really an issue, as by that time, she was very old, blind, deaf, etc. She basically ate, pottied, and slept. So having her in a cage for most of the day really wasn't a big deal - she would just sleep in her bed all day. The walking/attention she would get were plenty - for her.
That would not be the ideal situation for Lexi, though - a young, healthy puppy - or any other active, alert dog.
I asked around, and talked about it a lot. One friend actually offered to watch Lexi for me. I wasn't sure about it. I certainly trust her, but she does have a dog (an older Lhasa), and a daughter - although she's in high school already. I just don't know if people realize how careful you have to be with such a small dog! But she did offer to have me bring Lexi over to make sure the two dogs got along. I tucked that away if needed.
Another friend said she would have watched her, and would watch her another time, but she just couldn't do it for that weekend. I did go to the doggie "bed & breakfast" that she uses, and loves, though. But I wasn't happy with that. For what it was, it seemed clean, but like an older clean. All the little dogs were in crates stacked 3 high. They would get about an hour a day, outside, in a small cement-floored run surrounded by chain link fence. For an extra $25, you could have your dog played with in an enclosed playground area - one-on-one. That would be for 1/2 hour one day and 1/2 hour the next day. I just couldn't bear to leave her in a crate for that long! I'm sure the dogs are well-taken care of, but I want more for Lexi.
I was very fortunate that my brother agreed to stay at my house and watch Lexi for me. That worked out for both of us, but it would not be the solution every time.
Look into pet sitters. Some will come to visit your house maybe twice a day to walk, feed, and play with your pet. Ask around for recommendations. Ask a neighbor or friend/relative who lives nearby if they would be interested in doing this. I would be hesitant about letting a stranger into my home, but I know that there are many people who do that, and it works out fine for them.
I feel I just got very lucky, though... I went to a new groomer because I didn't care for the one who did Lexi's first grooming. She grooms small dogs, specializing in Yorkies. She raises Yorkies and breeds Yorkies and shows Yorkies. She also boards dogs at her house. While I was there (she grooms out of her house), she had one smaller dog - not sure what type, and a Yorkie. One had run of the kitchen; the other was gated in the den. While I was there, another Yorkie was dropped off. She was loose in the part of the house where we were - the dining room/living room area. The house was clean - it did not smell like dogs! They are obviously well-taken care of and loved. Some of the dogs who stay there sleep in the beds with the family members. I love that they are in a house setting, played with, and given lots of attention and affection from people who love Yorkies! Both my daughter and I felt that if we ever needed someone to watch Lexi, we would feel comfortable using her. (Oh, and in speaking to her, I found out she is a YT member too!)
So, talk to as many people as you can...you never know what you will find!
Good luck.