Which types of events can I bring my baby to? If the baby will scream or otherwise disrupt, I know it's a no-go, but what if she will sleep in her stroller the whole time or sit quietly on my lap, allowing me to participate and also to nurse her? I often have to choose between taking her with me to an event or just staying home. I've had to figure this out about board meetings, more casual planning meetings in someone's home, a fancy out of town wedding, a Bar Mitzvah and others. In terms of Jewish events, I find that the more Orthodox a setting is, the more acceptable it is to bring a little baby. Maybe this is because it is the norm for those families to have a nursing baby a lot of the time. In some cases, I have asked the host/person in charge. Other times I've just made my best guess. I don't want to seem too cheap for a babysitter or like I'm disrespecting the event, but sometimes I can't or don't want to leave the baby at home. Thoughts?
Bringing Along Baby
It sounds like you have great instincts about what is and isn't appropriate. You're not asking about taking a baby to the theater (never a good idea unless it's a show intended for children) or restaurants (depends) or to the park (obviously acceptable), so you've hit on the gray areas where the answer varies based on who's hosting, time of day, baby's temperment and a million other factors.
Meetings: If you think you can do a reasonable job being present for the meeting with your baby there, go for it. Ask permission in advance if it's in someone else's home and clear it with the facilitator. Also plan an exit strategy if you need to step away. If you're running the meeting, you have a lot of leeway to set the tone, but you also have more responsibility to keep things moving without a debilitating amount of disruption. If the baby will definitely be asleep, that helps. Or, if you can wear the baby for instant soothing, that's also a way to go. If you know the baby will need to nurse at some point, you could arrange the agenda to include a break or for someone else to lead a particular part of the discussion. I have, in fact, led meetings while nursing, and while some people are skilled at such multi-tasking, those were not my favorite experiences of motherhood thus far. On the other hand, if you pull it off successfully, you feel like Superwoman! One-on-one meetings can actually be great with a baby, again, as long as you clear it with the other person, but it's a good way to get the conversation started.
Bar Mitzvahs: The same rules apply here as for any Shabbat or holiday in synagogue. These include bringing quiet toys and, depending on the baby's age, lots of snacks. Wearing the baby is also helpful for naps and comforting without having to leave services. If you expect to have to leave, particularly to nurse, ask someone who knows the synagogue where they recommend going, and then be prepared to slip away. I have also nursed during services, but again, you have to be in a congregation where people are going to allow you to feel comfortable. If it's an out of town Bar Mitzvah, you might not be able to gauge this in advance, so be prepared for a variety of scenarios. In terms of the Bar Mitzvah party, unless it's an afternoon affair in the synagogue social hall, in which case, I would expect that bringing a baby would be fine, the same rules apply as for weddings. See below.
Fancy out of town weddings: If it were just "fancy wedding," my gut says leave the baby home, but with the out of town bit added in, you have a very strong case for bringing the baby. Finding a babysitter where you live is tough enough, finding one in another city to come to a hotel room is awfully, maybe even prohibitively, difficult. You really have to talk to the couple getting married. Maybe they're already arranging for childcare for other families and you can tag onto that. Maybe there are four other babies coming, and they've planned for you to sit at a table with all of them. If the wedding is in a location where a sitter could have the baby in the lobby and then bring her to you for nursing, that's an option. You could also inquire about bringing another friend or family member with you to be on baby duty. If you're not so close with the couple, this might just be an affair that you need to miss because of all of the logistical complications. If you are very close, hopefully they'll understand and help you make the appropriate arrangements. I have brought kids to weddings (and nursed them there!). I have also received wedding invitations that included my kids and opted instead for a babysitter so that my husband and I could have a night out.
In any of these cases, as long as you've cleared it with the host, it's no one else's business whether you're bringing the baby because you don't want to pay for childcare or because it's easier for nursing or for whatever other reason. There will also be times as a mother where you do actually have to choose between being with the baby and going to a meeting or event. Those choices can be tough, but they can also help you clarify your priorities at a particular time. If you opt for being home with the baby, try to do so in a way that you won't resent or regret later. If you opt for the event, be fully present and don't spend the whole time texting the sitter or showing pictures to other guests. Whatever choice you make, try to put it within the context of a full life of spending time with your kids and also participating fully in your community. That way, no one event or decision will feel like it determines your long term social or professional life.