Montmartre is perfectly safe, though parts of it could be described as "seedy." The bigger question, though, is why you'd want to be so far out from the city center - unless your conference is in the Montmartre area, which seems unlikely.

It's primarily based on prices... the conference is in the Saint Germain area and I don't mind staying a little farther out. I've found other places more centrally located but are either more expensive or really small or have a sofa bed.
I'm traveling with my boyfriend and we hope to cook a few meals in the apartment.

If your conference is in St-Germain then I would stay there or nearby. I like that area much better than Montmartre. Spend a bit more money and get a place with a real bed.

Have you looked at the Paris Apartment thread on this board? It's full of recommendations.

If you're going for a conference isn't your employer paying for lodging and meals?

Factor in the time and money spent getting back and forth from St-Germain to Montmartre and maybe it's not such a bargain.

@ Adrienne: I did look through that thread and there are a few recommended places in the area that I'm looking at as well as St-Germain. A lot of the other ones are out of my price range. It is true that my employer will pay for the lodging but there is a budget for that too. The less I spend on lodging the more I can spend on food and other expenses. How expensive is the metro?

Try looking in the 5th instead of the 6th...you might find something towards Montparnasse or the rue Monge area. That would keep you within walking distance of St-Germain. I don't know what your budget is, but during my apartment search this year I came across a lot of apartments that were located in those areas that I felt were too far from my target zone, but would certainly be more convenient for you than staying on the other side of Paris in Montmartre.

I don't like St Germain that well myself, but wouldn't stay in MOntmartre, it's too inconvenient. I really wouldn't stay there if I had to go to a conference in St Germain daily. There are plenty of areas of Paris other than those two.

Montmartre isn't less touristy when you are around Sacre Coeur, exactly the opposite. It would be safe, I'm sure, unless your boyfriend likes to pick up hookers or go into sex places.

I've stayed ON Rue Chappe and totally loved it. It was a very nice area and felt very neighborhoody (i.e. not touristy), despite its proximity to Sacre Couer. It's very hilly, like many parts of Montmartre - just a heads-up, but it took us no time at all to get used to it. You'll be close to Rue Lepic and Rue des Martyrs, where you can buy provisions for cooking.

Enjoy!

<< I'm traveling with my boyfriend and we hope to cook a few meals in the apartment. >>

Here are some things to think about (I'm assuming your conference is all day for a week?):

After being in a conference I wouldn't want to go back to the apartment and cook and spend more time inside. There are inexpensive restaurants and cafes you can eat at if you're on a budget (assuming you're cooking to save money).

You'll spend at least 30 minutes each way in a crowded subway. After the conference you'll go back to the apartment in the Montmartre area to change. Then you'll get back on the metro to come back in the evening to the 4th, 5th, 6th area to experience the many things in that area.

Think about being able to walk out your door, walking to the conference and seeing something of Paris on the way. You could take a slightly different route each time.

If you were not in Paris for work, the Montmartre area would probably be ok (although it would not even be my 5th choice for location). Since you're working you'll have a limited amount of time to experience Paris and do some sightseeing in the evenings, even if it's just walking around and looking at the beautiful buildings all lit up. You'll want to be someplace central to do this.

The metro is cheap - about E12 for a carnet (10 tickets). It's about the time you'll spend commuting underground rather than enjoying Paris above ground.