Who was Mikael Blomkvist with at the end of the movie and why did Lisbeth hate it so much?

Can't remember the movie exactly, but in the book it's Erika Berger:

Now, here's another non-boring aspect of the ending, and the part which leaves us scrambling to get to the next book. Something important happens to Salander – she discovers she's in love (for the first time ever!) with Blomkvist.

So, what does she do? She tries to love, and it takes much more courage than it did to steal millions of dollars or to golf-club a serial killer. She goes and buys Blomkvist a present, so she'll have an excuse to visit him and tell him of her love. Inspired by his love for Elvis, she buys him a metal sign featuring the King and the words "Heartbreak Hotel." A fittingly ironic present given the circumstances, right?

But then it turns out to be not so ironic. Salander see Blomkvist with Erika Berger on their way for a love tryst (should've called first!) and her jealousy valve and fragile heart almost crash to pieces in the Stockholm streets.

This is Salander we're talking about so, no, she doesn't save the Elvis sign to give to him later, and then return to her place to calmly wait for another time when Blomkvist's more available. Rather, she tosses the Elvis in the trash. And that's how it ends.

Aha, in the movie it's also Erika:

In the powerful ending scene Lisbeth goes to see Mikael, carrying along a gift - a leather jacket just like she saw him wear in one of the photos from his youth. When she gets to her destination she sees Mikael leaving his place along with Erika, his girlfriend, whom he hugs. As Lisbeth is watching them you can see the heartbreak in her eyes and the sense she doesn't feel like she belongs in Mikael's life anymore, along with realization - she never really did. She walks away, throws the gift in the trash and leaves while gorgeous "What if we could?" plays in the background.

Just to add to @BCdotWEB's excellent answer.

The passage in the book provides some context and reads:

She had no faith in herself. Blomkvist lived in a world populated by people with respectable jobs, people with orderly lives and lots of grown-up points. His friends did things, went on TV, and shaped the headlines. What do you need me for? Salander’s greatest fear, which was so huge and so black that it was of phobic proportions, was that people would laugh at her feelings. And all of a sudden all her carefully constructed self-confidence seemed to crumble.

That’s when she made up her mind. It took her several hours to mobilise the necessary courage, but she had to see him and tell him how she felt.

Anything else would be unbearable.

She needed some excuse to knock on his door. She had not given him any Christmas present, but she knew what she was going to buy. In a junk shop she had seen a number of metal advertising signs from the fifties, with embossed images. One of the signs showed Elvis Presley with a guitar on his hip and a cartoon balloon with the words HEARTBREAK HOTEL. She had no sense for interior design, but even she could tell that the sign would be perfect for the cabin in Sandhamn. It cost 780 kronor, and on principle she haggled and got the price knocked down to 700. She had it wrapped, put it under her arm, and headed over to his place on Bellmansgatan.

At Hornsgatan she happened to glance towards Kaffebar and saw Blomkvist coming out with Berger in tow. He said something, and she laughed, putting her arm around his waist and kissing his cheek. They turned down Brännkyrkagatan in the direction of Bellmansgatan. Their body language left no room for misinterpretations — it was obvious what they had in mind.

The pain was so immediate and so fierce that Lisbeth stopped in mid-stride, incapable of movement. Part of her wanted to rush after them. She wanted to take the metal sign and use the sharp edge to cleave Berger’s head in two. She did nothing as thoughts swirled through her mind. Analysis of consequences. Finally she calmed down.

“What a pathetic fool you are, Salander,” she said out loud.

She turned on her heel and went home to her newly spotless apartment. As she passed Zinkensdamm, it started to snow. She tossed Elvis into a dumpster.

^{The Girl With The Dragon Tattoo - Steig Larsson}

It's at the this point...the book ends..so there is no additional analysis. I haven't read the sequel in some time but it's just been added to my list.